A094787 - OEIS

%I #12 Sep 08 2022 08:45:13

%S 3,2,5,5,3,2,2,17,7,17,5,13,3,2,17,11,19,7,13,5,11,3,2,3,2,23,5,53,3,

%T 2,5,17,3,2,29,13,107,11,61,41,23,7,101,5,19,3,2,73,79,31,13,29,11,67,

%U 73,113,7,23,5,61,3,2,37,17,79,59,61,13,31,11,29,53,71,7,53,5,23,3,2,41,19

%N a(n) = smallest prime p such that p + n is a perfect power m^k, k >= 2.

%C Conjecture: every prime is contained in this sequence.

%e 2+8=10, 3+8=11, 5+8=13, 7+8=15, 11+8=19, 13+8, 17+8=25. 17 is the first prime that when added to 8 gives a perfect power, viz. 25.

%p A094787 := proc(n)

%p     local i ;

%p     for i from 1 do

%p         if isA001597(ithprime(i)+n) then

%p             return ithprime(i) ;

%p         end if;

%p     end do:

%p end proc:

%p seq(A094787(n),n=1..40) ; # _R. J. Mathar_, Nov 15 2019

%o (PARI) k(n,m) = for(j=1,m, forprime(x=2,n,if(ispower(x+j),print1(x",");break))) ispower(n) = { local(p,r,j); r = sqrt(n); for(j=2,floor(r), p = floor(log(n)/log(j)+.5); if(j^p ==n,return(1)); ); return(0) }

%o (Magma) a:=[]; for n  in [1..81] do p:=2; while not IsPower(p+n) do p:=NextPrime(p); end while; Append(~a,p); end for; a; // _Marius A. Burtea_, Nov 15 2019

%K nonn

%O 1,1

%A _Cino Hilliard_, Jun 10 2004

%E Offset corrected by _R. J. Mathar_, Nov 15 2019