A196815 Smallest index k such that prime(k+n) - prime(k) is a perfect square.

1, 2, 14, 1, 4, 2, 18, 9, 7, 3, 29, 21, 19, 12, 8, 4, 2, 31, 21, 19, 11, 1, 59, 4, 2, 22, 24, 15, 16, 8, 6, 3, 36, 37, 174, 21, 18, 11, 12, 63, 78, 189, 38, 2, 27, 25, 112, 1, 107, 12, 6, 4, 45, 169, 28, 33, 21, 112, 14, 9, 10, 6, 4, 44, 37, 153, 151, 29, 27

Offset

1,2

Comments

The corresponding primes are in A196874.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(1) = 1 because prime(1) = 2 is the initial prime of a subset of 2 consecutive primes {2, 3} such that 3 - 2 = 1 = 1^2;
a(3) = 14 because prime(14) = 43 is the initial prime of a subset of 4 consecutive primes {43, 47, 53, 59} such that 59 - 43 = 16 = 4^2.

Maple

A196815 := proc(n)
        for k from 1 do
                if issqr(ithprime(k+n)-ithprime(k)) then
                        return k;
                end if;
        end do:
end proc:
seq(A196815(n), n=1..80) ; # R. J. Mathar, Oct 06 2011

Mathematica

spk[n_]:=Module[{k=1}, While[!IntegerQ[Sqrt[Prime[n+k]-Prime[k]]], k++]; k]; Array[spk, 70] (* Harvey P. Dale, Jul 23 2012 *)

Prog

(PARI) a(n) = {my(k=1); while (! issquare(prime(k+n)- prime(k)), k++); k; } \\ Michel Marcus, Dec 28 2015

Crossrefs

Cf. A000040.

Sequence in context: A249510 A324219 A349877 * A260120 A368758 A221234

Adjacent sequences: A196812 A196813 A196814 * A196816 A196817 A196818

Keyword

nonn

Author

Michel Lagneau, Oct 06 2011

Status

approved