A295405 - OEIS

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A295405

a(n) = 1 if n^2+1 is prime, 0 otherwise.

3

1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1

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OFFSET

1

COMMENTS

It is conjectured that n^2+1 is prime infinitely often.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000 (first 10000 terms from Simon Plouffe)

Index entries for characteristic functions

FORMULA

a(n) = A010051(A002522(n)). - Robert Israel, Nov 22 2017

EXAMPLE

With n=1, a(1) = 2, n=2, a(2) = 5, a(3) = 0 since 10 is not prime.

MAPLE

seq(`if`(isprime(n^2+1), 1, 0), n=1..100); # Robert Israel, Nov 22 2017

MATHEMATICA

Boole[PrimeQ[Range[150]^2+1]] (* Paolo Xausa, Feb 23 2024 *)

PROG

(PARI) a(n)=isprime(n^2+1)

CROSSREFS

Characteristic function of A005574.

Cf. A002496, A002522, A010051.

Cf. also A355449.

Sequence in context: A323509 A197183 A357382 * A267001 A141735 A343999

Adjacent sequences: A295402 A295403 A295404 * A295406 A295407 A295408

KEYWORD

nonn

AUTHOR

Simon Plouffe, Nov 22 2017

EXTENSIONS

Data section extended up to term a(120) by Antti Karttunen, Jul 12 2022

STATUS

approved