Search: a335592 -id:a335592
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4, 17, 27, 53, 74, 91, 97, 108, 111, 139, 152, 171, 207, 242, 245, 247, 275, 280, 286, 292, 310, 323, 352, 355, 385, 398, 424, 430, 471, 476, 484, 504, 525, 551, 555, 561, 586, 615, 626, 658, 659, 705, 709, 736, 744, 754, 772, 823, 837, 841, 849, 858, 866, 869, 870, 877, 882, 896, 937, 960, 995
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(3) = 27 is a term because A335592(27) = det(631, 563; 577, 619) = 65738 = 2*32869 and 32869 is prime.
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MAPLE
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count:= 0: R:= NULL:
L:= [-9, -7, -3, -1]:
for k from 1 while count < 100 do
for i from 1 to 4 do
for x from L[i]+10 by 10 do until isprime(x);
L[i]:= x;
od;
v:= L[1]*L[4]-L[2]*L[3];
if isprime(abs(v)/2) then count:= count+1; R:= R, k; fi
od:
R;
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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1399, 17939, 32869, 149759, 282349, 458929, 388099, 615389, 634169, 585619, 926179, 1053449, 1876339, 1336529, 2056829, 2156369, 2695249, 2653699, 2819779, 2501449, 1461709, 2176679, 3457969, 2549479, 3433819, 5299219, 4845499, 4774619, 7874749, 8796049, 9139469, 9029399, 7075759, 5156299
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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All terms end in 9 (or 1, if there are any with A335592(k) < 0).
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LINKS
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FORMULA
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EXAMPLE
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A335593(3) = 27, A335592(27) = det(631, 563; 577, 619) = 65738 = 2*32869
so a(3) = 32869.
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MAPLE
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count:= 0: R:= NULL:
L:= [-9, -7, -3, -1]:
for k from 1 while count < 100 do
for i from 1 to 4 do
for x from L[i]+10 by 10 do until isprime(x);
L[i]:= x;
od;
v:= L[1]*L[4]-L[2]*L[3];
if isprime(abs(v)/2) then count:= count+1; R:= R, abs(v)/2; fi
od:
R;
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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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A337145
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a(n) is the determinant of the 2 X 2 matrix whose entries (when read by rows) are the n-th primes congruent to 1, 3, 5, 7 mod 8 respectively.
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+10
3
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104, 800, 1712, 2592, 3760, 4840, 5728, 12848, 15664, 18424, 20888, 23520, 28232, 28560, 25320, 30280, 37248, 50520, 43680, 33664, 61560, 73920, 70544, 57696, 38696, 27408, 79280, 63392, 107328, 109536, 162608, 172296, 187352, 197040, 248064, 228320, 215912, 229152, 255480, 231304, 286408, 256320
(list;
graph;
refs;
listen;
history;
text;
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OFFSET
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1,1
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COMMENTS
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The first negative term is a(20750) = -58207896.
All terms are divisible by 8.
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LINKS
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EXAMPLE
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The first primes == 1, 3, 5, 7 (mod 8) are 17, 3, 5, 7 respectively, so a(1) = 17*7 - 3*5 = 104.
The second primes == 1, 3, 5, 7 (mod 8) are 41, 11, 13, 23 respectively, so a(2) = 41*23 - 11*13 = 800.
The third primes == 1, 3, 5, 7 (mod 8) are 73, 19, 29, 31 respectively, so a(3) = 73*31 - 19*29 = 1712.
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MAPLE
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R:= NULL:
L:= [-7, -5, -3, -1]:
found:= false:
for k from 1 to 100 do
for i from 1 to 4 do
for x from L[i]+8 by 8 do until isprime(x);
L[i]:= x;
od;
v:= L[1]*L[4]-L[2]*L[3];
R:= R, v;
od:
R;
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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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