A056895 -id:A056895 - cp's OEIS frontend

A056898 a(n) = smallest number m such that m^2+n is prime.

1, 0, 0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 0, 3, 2, 1, 0, 1, 0, 3, 4, 1, 0, 7, 2, 9, 2, 1, 0, 1, 0, 3, 2, 3, 6, 1, 0, 3, 2, 1, 0, 1, 0, 3, 4, 1, 0, 5, 2, 3, 4, 1, 0, 5, 2, 9, 2, 1, 0, 1, 0, 3, 2, 3, 6, 1, 0, 9, 2, 1, 0, 1, 0, 3, 2, 5, 6, 1, 0, 3, 4, 1, 0, 5, 2, 9, 4, 1, 0, 7, 4, 3, 2, 3, 6, 1, 0, 3, 2

Offset: 1

Henry Bottomley, Jul 05 2000

nonn

			a(8) = 3 since 3^2+8 = 17 which is prime.

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000040, A002496, A056892, A056893, A056894, A056895, A056896, A056897.

A056898(n) = { my(m=0); while(!isprime((m*m)+n),m++); (m); }; \\ Antti Karttunen, Mar 04 2018

a(n) = sqrt(A056896(n)-n) = sqrt(A056897(n)).

For p a prime: a(p) = 0 (and a(p-1) = 1 if p<>3).

A056894 If the smallest prime with a square excess of n is p then a(n)=p-n.

Original entry on oeis.org

1, 1, 4, 9, 36, 25, 16, 81, 64, 49, 36, 49, 100, 225, 64, 81, 576, 121, 144, 441, 256, 169, 144, 169, 256, 225, 196, 289, 324, 961, 400, 729, 400, 529, 324, 361, 484, 441, 400, 529, 576, 529, 576, 729, 784, 841, 900, 625, 1444, 1521, 676, 961, 900, 1225, 784

Offset: 1

Henry Bottomley, Jul 05 2000

nonn

			a(4)=9 because the smallest prime with a square excess of 4 is 13 and 13-4=9

Cf. A000040, A000196, A002496, A048760, A053186, A056892-A056898.

a(n) = A056893(n) - n = A048760(A056893(n)) = A056895(n)^2

cp's OEIS Frontend

A056898 a(n) = smallest number m such that m^2+n is prime.

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