Search: a002261 -id:a002261
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A050529
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Primes of form 11*2^n+1.
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+10
4
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23, 89, 353, 1409, 5767169, 23068673, 96757023244289, 26596368031521841843535873, 467888254516290387262140085218681290753, 1871553018065161549048560340874725163009, 9050275065266633231852330504065427777405047260984689248417349633
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OFFSET
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1,1
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LINKS
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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A001772
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Numbers k such that 11*2^k - 1 is prime.
(Formerly M2145 N0854)
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+10
3
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2, 26, 50, 54, 126, 134, 246, 354, 362, 950, 1310, 2498, 6926, 11826, 31734, 67850, 74726, 96150, 374114, 696438, 743322, 1044086, 1104606, 1261478
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OFFSET
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1,1
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REFERENCES
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H. Riesel, "Prime numbers and computer methods for factorization", Progress in Mathematics, Vol. 57, Birkhäuser, Boston, 1985, Chap. 4, see pp. 381-384.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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PROG
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(Python)
from sympy import isprime
def aupto(lim): return [k for k in range(1, lim+1) if isprime(11*2**k - 1)]
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CROSSREFS
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KEYWORD
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hard,nonn,nice,more
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AUTHOR
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EXTENSIONS
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More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
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STATUS
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approved
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A322302
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Primes p such that 11*2^p + 1 is also prime.
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+10
0
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OFFSET
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1,1
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COMMENTS
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LINKS
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MAPLE
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select(p->isprime(p) and isprime(11*2^p+1), [$1..1000]); # Muniru A Asiru, Dec 20 2018
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MATHEMATICA
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Select[Prime[Range[1000]], PrimeQ[11 2^# + 1] &]
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PROG
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(Magma) [p: p in PrimesUpTo (6000) | IsPrime(11*2^p+1)];
(GAP) Filtered([1..1000], p -> IsPrime(p) and IsPrime(11*2^p+1)); # Muniru A Asiru, Dec 20 2018
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A361076
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Array, read by ascending antidiagonals, whose n-th row consists of the powers of 2, if n = 1; of the primes of the form (2*n-1)*2^k+1, if they exist and n > 1; and of zeros otherwise.
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+10
0
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1, 1, 2, 1, 2, 4, 2, 3, 5, 8, 1, 4, 7, 6, 16, 1, 2, 6, 13, 8, 32, 2, 3, 3, 14, 15, 12, 64, 1, 8, 5, 6, 20, 25, 18, 128, 3, 2, 10, 7, 7, 26, 39, 30, 256, 6, 15, 4, 20, 19, 11, 50, 55, 36, 512, 1, 10, 27, 9, 28, 21, 14, 52, 75, 41, 1024, 1, 4, 46, 51, 10, 82, 43, 17, 92, 85, 66, 2048
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OFFSET
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1,3
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COMMENTS
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LINKS
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EXAMPLE
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Table starts
2 8 10 20 28 82 188 308 ... A032356
...
(2*39279 - 1)*2^r + 1 is composite for every r > 0 (see comments from A046067), so the 39279th row is A000004, the zero sequence.
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PROG
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(PARI) vk(k, nn) = if (k==1, return (vector(nn, i, 2^(i-1)))); my(v = vector(nn-k+1), nb=0, i=0, x); while (nb != nn-k+1, if (isprime((2*k-1)*2^i+1), nb++; v[nb] = i); i++; ); v;
lista(nn) = my(v=vector(nn, k, vk(k, nn))); my(w=List()); for (i=1, nn, for (j=1, i, listput(w, v[i-j+1][j]); ); ); Vec(w); \\ Michel Marcus, Mar 03 2023
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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