A056895 If the smallest prime with a square excess of n is p then a(n)^2 = p - n.

1, 1, 2, 3, 6, 5, 4, 9, 8, 7, 6, 7, 10, 15, 8, 9, 24, 11, 12, 21, 16, 13, 12, 13, 16, 15, 14, 17, 18, 31, 20, 27, 20, 23, 18, 19, 22, 21, 20, 23, 24, 23, 24, 27, 28, 29, 30, 25, 38, 39, 26, 31, 30, 35, 28, 45, 34, 31, 42, 31, 34, 33, 32, 33, 36, 35, 34, 75, 40, 37, 36, 41, 48, 45

Offset

1,3

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Formula

a(n) = sqrt(A056893(n)-n) = A000196(A056893(n)) = sqrt(A056894(n)).

Example

a(4)=3 because the smallest prime with a square excess of 4 is 13 and 13 - 4 = 3^2.

Mathematica

a = {}; Do[p = 2; While[n != p - (r = Floor@Sqrt[p])^2, p = NextPrime[p]]; AppendTo[a, r], {n, 74}]; a (* Ivan Neretin, May 02 2019 *)

Prog

(PARI) a(n) = {my(p=2); while(n != p-sqrtint(p)^2, p = nextprime(p+1)); sqrtint(p - n); } \\ Michel Marcus, May 05 2019

Crossrefs

Cf. A000040, A000196, A002496, A048760, A053186.

Cf. A056892, A056893, A056894, A056896, A056897, A056898.

Sequence in context: A166166 A106452 A254118 * A254117 A370629 A218890

Adjacent sequences: A056892 A056893 A056894 * A056896 A056897 A056898

Keyword

nonn

Author

Henry Bottomley, Jul 05 2000

Status

approved