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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.
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%I #15 Sep 29 2024 11:57:11

%S 11235,11253,11325,11352,11523,11532,21135,21153,23115,23511,25113,

%T 25311,31125,31152,32115,32511,35112,35211,51123,51132,52113,52311,

%U 53112,53211,111235,111253,111325,111352,111523,111532,112135,112153,112235,112253

%N 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 Robert Israel, <a href="/A135015/b135015.txt">Table of n, a(n) for n = 1..10000</a> (first 300 terms from David Applegate)

%p filter:= proc (n) local L, LP;

%p L := convert(n, base, 10);

%p if has(L, 0) then return false end if;

%p if has(L, 1) and not has(L, 2) then return false end if;

%p if has(L, 2) and not has(L, 3) then return false end if;

%p if has(L, 3) and not has(L, 5) then return false end if;

%p if has(L, 4) and not has(L, 7) then return false end if;

%p LP := [seq([L[i], L[i+1]], i = 1 .. nops(L)-1)];

%p if has(L, 5) and not member([1, 1], LP) then return false end if;

%p if has(L, 6) and not member([3, 1], LP) then return false end if;

%p if has(L, 7) and not member([7, 1], LP) then return false end if;

%p if has(L, 8) and not member([9, 1], LP) then return false end if;

%p if has(L, 9) and not member([3, 2], LP) then return false end if;

%p true

%p end proc:

%p select(filter, [$1..1.5*10^5]);

%o (C++) // For C++ program see the Applegate link in A135463.

%Y Cf. A134692, A134698, A134962.

%K nonn,base,look

%O 1,1

%A _David Applegate_ and _N. J. A. Sloane_, Feb 10 2008