cp's OEIS Frontend

A135015 Numbers n with property that for each single digit d of n, we can also see the decimal expansion of the d-th prime as a substring of n. Also n may not contain any zero digits.

%I A135015 #15 Sep 29 2024 11:57:11
%S A135015 11235,11253,11325,11352,11523,11532,21135,21153,23115,23511,25113,
%T A135015 25311,31125,31152,32115,32511,35112,35211,51123,51132,52113,52311,
%U A135015 53112,53211,111235,111253,111325,111352,111523,111532,112135,112153,112235,112253
%N A135015 Numbers n with property that for each single digit d of n, we can also see the decimal expansion of the d-th prime as a substring of n. Also n may not contain any zero digits.
%H A135015 Robert Israel, <a href="/A135015/b135015.txt">Table of n, a(n) for n = 1..10000</a> (first 300 terms from David Applegate)
%p A135015 filter:= proc (n) local L, LP;
%p A135015   L := convert(n, base, 10);
%p A135015   if has(L, 0) then return false end if;
%p A135015 if has(L, 1) and not has(L, 2) then return false end if;
%p A135015 if has(L, 2) and not has(L, 3) then return false end if;
%p A135015 if has(L, 3) and not has(L, 5) then return false end if;
%p A135015 if has(L, 4) and not has(L, 7) then return false end if;
%p A135015 LP := [seq([L[i], L[i+1]], i = 1 .. nops(L)-1)];
%p A135015 if has(L, 5) and not member([1, 1], LP) then return false end if;
%p A135015 if has(L, 6) and not member([3, 1], LP) then return false end if;
%p A135015 if has(L, 7) and not member([7, 1], LP) then return false end if;
%p A135015 if has(L, 8) and not member([9, 1], LP) then return false end if;
%p A135015 if has(L, 9) and not member([3, 2], LP) then return false end if;
%p A135015 true
%p A135015 end proc:
%p A135015 select(filter, [$1..1.5*10^5]);
%o A135015 (C++) // For C++ program see the Applegate link in A135463.
%Y A135015 Cf. A134692, A134698, A134962.
%K A135015 nonn,base,look
%O A135015 1,1
%A A135015 _David Applegate_ and _N. J. A. Sloane_, Feb 10 2008