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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A341406 A342937 A254027 * A318651 A083529 A102208

Adjacent sequences:  A284343 A284344 A284345 * A284347 A284348 A284349

KEYWORD

nonn

AUTHOR

Lars-Erik Svahn, Mar 25 2017

STATUS

approved

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Last modified April 17 11:08 EDT 2021. Contains 343064 sequences. (Running on oeis4.)