cp's OEIS Frontend

A378491 Numbers k such that (in base 10) the k-th composite is a substring of the k-th prime.

%I A378491 #14 Dec 09 2024 17:48:32
%S A378491 5738,20393,20397,20532,28566,305037,511920,151810713,27746745416,
%T A378491 60097588222
%N A378491 Numbers k such that (in base 10) the k-th composite is a substring of the k-th prime.
%C A378491 Numbers k such that A002808(k) is a substring of A000040(k).
%F A378491 floor((A000040(k) mod 10^i)/10^j) = A002808(k) for some i and j.
%e A378491 a(1) = 5738 is a term because the 5738th composite, 6591, is a substring of the 5738th prime, 56591.
%e A378491 a(2) = 20393 is a term because the 20393th composite, 22954, is a substring of the 20393th prime, 229547.
%p A378491 g:= proc(p,c) StringTools:-Search(sprintf("%d",c),sprintf("%d",p)) <> 0 end proc:
%p A378491 nextcomp:= proc(c) if isprime(c+1) then c+2 else c+1 fi end proc:
%p A378491 p:= 1: c:= 2: Res:= NULL:
%p A378491 for n from 1 to 10^6 do
%p A378491   p:= nextprime(p); c:= nextcomp(c);
%p A378491   if g(p,c) then Res:= Res,n; fi
%p A378491 od:
%p A378491 Res;
%Y A378491 Cf. A000040, A002808, A378479.
%K A378491 nonn,base,more
%O A378491 1,1
%A A378491 _Robert Israel_, Nov 28 2024
%E A378491 a(9) from _Michael S. Branicky_, Dec 06 2024
%E A378491 a(10) from _Michael S. Branicky_, Dec 09 2024