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A168167 Numbers with d digits (d>0) which have at least 2d distinct primes as substrings.

%I A168167 #11 Nov 12 2020 05:18:02
%S A168167 1373,3137,3797,5237,6173,11317,11373,13733,13739,13797,17331,19739,
%T A168167 19973,21137,21317,21373,21379,22397,22937,23117,23137,23173,23371,
%U A168167 23373,23719,23797,23971,24373,26173,26317,27193,27197,29173,29537
%N A168167 Numbers with d digits (d>0) which have at least 2d distinct primes as substrings.
%C A168167 "Substrings" includes the whole number in itself.
%C A168167 The terms up to 11317 are primes themselves. The subsequence A168169 lists primes which have more than 2d prime substrings.
%C A168167 From _Robert Israel_, Nov 11 2020: (Start)
%C A168167 Palindromes in the sequence include 1337331, 1375731, and 1793971.
%C A168167 Even numbers in the sequence include 313732, 313792 and 1131712. (End)
%H A168167 Robert Israel, <a href="/A168167/b168167.txt">Table of n, a(n) for n = 1..2500</a>
%e A168167 The least number with d digits to have 2d distinct prime substrings is a(1)=1373, with 4 digits and #{3, 7, 13, 37, 73, 137, 373, 1373} = 8.
%p A168167 filter:= proc(n) local i,j,count,d,S,x,y;
%p A168167   d:= ilog10(n)+1;
%p A168167   count:= 0; S:= {};
%p A168167   for i from 0 to d-1 do
%p A168167     x:= floor(n/10^i);
%p A168167     for j from i to d-1 do
%p A168167       y:= x mod 10^(j-i+1);
%p A168167       if not member(y,S) and isprime(y) then count:= count+1; S:= S union {y}; if count = 2*d then return true fi fi
%p A168167   od od;
%p A168167   false
%p A168167 end proc:
%p A168167 select(filter, [$10..10^5]); # _Robert Israel_, Nov 11 2020
%o A168167 (PARI) {for( p=1, 1e6, #prime_substrings(p) >= #Str(p)*2 & print1(p", "))} /* see A168168 for prime_substrings() */
%Y A168167 Cf. A069490, A131648, A012884, A168168, A168169.
%K A168167 nonn,base
%O A168167 1,1
%A A168167 _M. F. Hasler_, Nov 28 2009