A168169 Primes with d digits (d>0) which have more than 2d distinct primes as substrings.

23719, 31379, 52379, 113171, 113173, 113797, 123719, 153137, 179719, 199739, 211373, 213173, 229373, 231197, 231379, 233113, 233713, 236779, 237331, 237619, 237971, 241973, 259397, 291373, 313739, 317971, 327193, 337397, 343373, 353173

Offset

1,1

Comments

"Substrings" includes the whole number in itself.

This is a subsequence of A168167.

The least palindrome in this sequence is 9179719.

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

The least number with d digits to have over 2d distinct prime substrings is the prime a(1)=23719, with 5 digits and #{2, 3, 7, 19, 23, 37, 71, 719, 2371, 3719, 23719} = 11.

Maple

filter:= proc(n) local i, j, count, d, S, x, y;
  if not isprime(n) then return false fi;
  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, [seq(i, i=1..10^6, 2)]); # Robert Israel, Nov 11 2020

Prog

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

Crossrefs

Cf. A093301, A069490, A131648, A012884, A168167, A168168.

Sequence in context: A200437 A223342 A179918 * A344377 A031649 A011254

Adjacent sequences: A168166 A168167 A168168 * A168170 A168171 A168172

Keyword

nonn,base

Author

M. F. Hasler, Nov 28 2009

Status

approved