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

1,1

Comments

n is odd iff a(n) is even.

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.

Example

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.

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 *)

Prog

(ANS-Forth)
s" numbertheory.4th" included
: Gauss_twin \ n -- a(n)
  locals| n | 0
  begin 1+ dup dup * n dup * + isprime
     over 1+ dup * n 1+ dup * + isprime and
  until ;
(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

Crossrefs

Cf. A069003, A284211, A284327.

Sequence in context: A342937 A353571 A254027 * A318651 A083529 A102208

Adjacent sequences: A284343 A284344 A284345 * A284347 A284348 A284349

Keyword

nonn

Author

Lars-Erik Svahn, Mar 25 2017

Status

approved