|
%I #20 Dec 28 2015 16:58:31
%S 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,
%T 15,16,8,6,3,36,37,174,21,18,11,12,63,78,189,38,2,27,25,112,1,107,12,
%U 6,4,45,169,28,33,21,112,14,9,10,6,4,44,37,153,151,29,27
%N Smallest index k such that prime(k+n) - prime(k) is a perfect square.
%C The corresponding primes are in A196874.
%H Robert Israel, <a href="/A196815/b196815.txt">Table of n, a(n) for n = 1..10000</a>
%e 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;
%e 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.
%p A196815 := proc(n)
%p for k from 1 do
%p if issqr(ithprime(k+n)-ithprime(k)) then
%p return k;
%p end if;
%p end do:
%p end proc:
%p seq(A196815(n),n=1..80) ; # _R. J. Mathar_, Oct 06 2011
%t spk[n_]:=Module[{k=1},While[!IntegerQ[Sqrt[Prime[n+k]-Prime[k]]],k++];k]; Array[spk, 70] (* _Harvey P. Dale_, Jul 23 2012 *)
%o (PARI) a(n) = {my(k=1); while (! issquare(prime(k+n)- prime(k)), k++); k;} \\ _Michel Marcus_, Dec 28 2015
%Y Cf. A000040.
%K nonn
%O 1,2
%A _Michel Lagneau_, Oct 06 2011
|
