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

1373, 3137, 3797, 5237, 6173, 11317, 11373, 13733, 13739, 13797, 17331, 19739, 19973, 21137, 21317, 21373, 21379, 22397, 22937, 23117, 23137, 23173, 23371, 23373, 23719, 23797, 23971, 24373, 26173, 26317, 27193, 27197, 29173, 29537

Offset: 1

Author

M. F. Hasler, Nov 28 2009

Keywords

• nonn
• base

Comments

"Substrings" includes the whole number in itself.

The terms up to 11317 are primes themselves. The subsequence A168169 lists primes which have more than 2d prime substrings.

From Robert Israel, Nov 11 2020: (Start)

Palindromes in the sequence include 1337331, 1375731, and 1793971.

Even numbers in the sequence include 313732, 313792 and 1131712. (End)

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2500

Crossrefs

Cf. A069490, A131648, A012884, A168168, A168169.

Programs

Maple

filter:= proc(n) local i,j,count,d,S,x,y;
  d:= ilog10(n)+1;
  count:= 0; S:= {};
  for i from 0 to d-1 do
    x:= floor(n/10^i);
    for j from i to d-1 do
      y:= x mod 10^(j-i+1);
      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
  od od;
  false
end proc:
select(filter, [$10..10^5]); # Robert Israel, Nov 11 2020

PARI

{for( p=1, 1e6, #prime_substrings(p) >= #Str(p)*2 & print1(p", "))} /* see A168168 for prime_substrings() */