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A196815 Smallest index k such that prime(k+n) - prime(k) is a perfect square. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A219221 A249510 A324219 * A260120 A221234 A133420

Adjacent sequences:  A196812 A196813 A196814 * A196816 A196817 A196818

KEYWORD

nonn

AUTHOR

Michel Lagneau, Oct 06 2011

STATUS

approved

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Last modified October 16 13:51 EDT 2019. Contains 328093 sequences. (Running on oeis4.)