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

1,1

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)

Links

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

Example

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.

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

Prog

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

Crossrefs

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

Sequence in context: A060981 A140125 A179915 * A069490 A239974 A258964

Adjacent sequences: A168164 A168165 A168166 * A168168 A168169 A168170

Keyword

nonn,base

Author

M. F. Hasler, Nov 28 2009

Status

approved