A111488 Primes all of whose digits are triangular.

3, 11, 13, 31, 61, 101, 103, 113, 131, 163, 311, 313, 331, 601, 613, 631, 661, 1013, 1031, 1033, 1061, 1063, 1103, 1163, 1301, 1303, 1361, 1601, 1613, 1663, 3001, 3011, 3061, 3163, 3301, 3313, 3331, 3361, 3613, 3631, 6011, 6101, 6113, 6131, 6133, 6163

Offset

1,1

Comments

Includes all repunit primes (A004022). Conjecture: an infinite sequence. Note twin primes: (11, 13), (101, 103), (311, 313), (1031, 1033), (1061, 1063), (1301, 1303), (6131, 6133), (10301, 10303), (10331, 10333), (13001, 13003).

In other words, primes with digits in the set {0,1,3,6}. - M. F. Hasler, Jul 25 2015

The number of 1's in the representation must be either 1 or 2 (mod 3), because otherwise the number would be divisible by 3 (and therefore composite). The only exception is the 3 itself. This excludes basically members of A038603. - R. J. Mathar, Jul 25 2015

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

f:= proc(x) local L, p;
  L:= subs([3=6, 2=3], convert(x, base, 4));
  p:= add(L[i]*10^(i-1), i=1..nops(L));
  if isprime(p) then p fi
end proc:
map(f, [$1..4^4]); # Robert Israel, Dec 18 2018

Mathematica

Select[Prime@ Range@ 1000, SubsetQ[{0, 1, 3, 6}, IntegerDigits@ #] &] (* Michael De Vlieger, Jul 25 2015 *)

Prog

(PARI) A111488={(n, show=0, L=[0, 1, 3, 6])->my(t); for(d=1, 1e9, u=vector(d, i, 10^(d-i))~; forvec(v=vector(d, i, [1+(i==1&&!L[1]), #L]), ispseudoprime(t=vector(d, i, L[v[i]])*u)||next; show&print1(t", "); n--||return(t)))} \\ M. F. Hasler, Jul 25 2015

Crossrefs

Cf. A000040, A000217, A004022, A038603.

Cf. also A020450 - A020472, A036953, A260044, A260267 - A260271, A199325 - A199329, A061247, A199340 - A199349.

Sequence in context: A006559 A023248 A199341 * A125308 A260044 A199303

Adjacent sequences: A111485 A111486 A111487 * A111489 A111490 A111491

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Nov 15 2005

Extensions

Corrected by Ray Chandler, Nov 19 2005

Status

approved