A284346 a(n) is the least positive integer such that n^2 + a(n)^2 and (n + 1)^2 + (a(n) + 1)^2 are primes.
2, 1, 8, 1, 4, 1, 2, 3, 16, 3, 6, 7, 8, 1, 4, 1, 22, 5, 6, 3, 4, 17, 18, 5, 4, 1, 32, 5, 10, 29, 4, 27, 8, 15, 18, 1, 2, 15, 10, 3, 4, 247, 8, 15, 14, 19, 22, 35, 6, 19, 4, 27, 10, 11, 8, 1, 2, 5, 40, 13, 44, 127, 58, 61, 28, 1, 22, 13, 10, 19, 6, 7, 8, 15, 4, 9
Offset: 1
Keywords
Examples
a(1)=2 since (1 + 1)^2 + (1 + 1)^2 is not prime, but 1^2 + 2^2 = 5 and (1 + 1)^2 + (2 + 1)^2 = 13 are prime.
Links
- Lars-Erik Svahn, Table of n, a(n) for n = 1..10000
- Lars-Erik Svahn, numbertheory.4th
- Akshaa Vatwani, Bounded gaps between Gaussian primes, Journal of Number Theory, Volume 171, February 2017, Pages 449-473.
- Eric Weisstein's World of Mathematics, Gaussian Prime.
- Index entries for Gaussian integers and primes.
Programs
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Mathematica
Rest@ FoldList[Module[{k = 1}, While[Times @@ Boole@ Map[PrimeQ, {#2^2 + k^2, (#2 + 1)^2 + (k + 1)^2}] < 1, k++]; k] &, 1, Range@ 76] (* Michael De Vlieger, Mar 25 2017 *) -
PARI
a(n) = my(k=0); while (! (isprime(n^2+k^2) && isprime((n+1)^2+(k+1)^2)), k++); k; \\ Michel Marcus, Mar 25 2017
Comments