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A320028
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a(n) is the first prime encountered when running the Collatz algorithm (halving and tripling steps) on the number n.
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1
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2, 3, 2, 5, 3, 7, 2, 7, 5, 11, 3, 13, 7, 23, 2, 17, 7, 19, 5, 2, 11, 23, 3, 19, 13, 41, 7, 29, 23, 31, 2, 19, 17, 53, 7, 37, 19, 59, 5, 41, 2, 43, 11, 17, 23, 47, 3, 37, 19, 29, 13, 53, 41, 83, 7, 43, 29, 59, 23, 61, 31, 137, 2, 37, 19, 67, 17, 13, 53, 71, 7, 73, 37, 113, 19, 29, 59, 79, 5, 61, 41, 83, 2, 2, 43, 131
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OFFSET
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2,1
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COMMENTS
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A modified version of the halving and tripling Collatz algorithm, which stops as soon as the starting number becomes a prime (instead of stopping when the starting number reaches 1).
The plot of this sequence "completes" or "fills" the lower (empty) part of plot of A270570 and evolves in a similar fashion.
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LINKS
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FORMULA
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EXAMPLE
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a(4) is 2 because 4/2 = 2 and 2 is prime.
a(6) is 3 because 6/2 = 3 and 3 is prime.
a(15) is 23 because 15*3 + 1 = 46; 46/2 = 23 and 23 is prime.
a(18) is 7 because 18/2 = 9; 9*3 + 1 = 28; 28/2 = 14; 14/2 = 7 and 7 is prime.
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MATHEMATICA
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Array[NestWhile[If[EvenQ@ #, #/2, 3 # + 1] &, #, ! PrimeQ@ # &] &, 86, 2] (* Michael De Vlieger, Nov 07 2018 *)
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PROG
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(Java) int collatzPrime(int i) {
while(!BigInteger.valueOf(i).isProbablePrime(10) && i > 1) {
if(i % 2 == 0)
i /= 2;
else
i = 3 * i + 1;
}
return i;
}
(PARI) a(n) = {while (!isprime(n), if (n % 2, n = 3*n+1, n = n/2); ); n; } \\ Michel Marcus, Oct 28 2018
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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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