A111488 - OEIS

%I #18 Dec 18 2018 17:07:47

%S 3,11,13,31,61,101,103,113,131,163,311,313,331,601,613,631,661,1013,

%T 1031,1033,1061,1063,1103,1163,1301,1303,1361,1601,1613,1663,3001,

%U 3011,3061,3163,3301,3313,3331,3361,3613,3631,6011,6101,6113,6131,6133,6163

%N Primes all of whose digits are triangular.

%C 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).

%C In other words, primes with digits in the set {0,1,3,6}. - _M. F. Hasler_, Jul 25 2015

%C 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

%H Robert Israel, <a href="/A111488/b111488.txt">Table of n, a(n) for n = 1..10000</a>

%p f:= proc(x) local L,p;

%p   L:= subs([3=6,2=3],convert(x,base,4));

%p   p:= add(L[i]*10^(i-1),i=1..nops(L));

%p   if isprime(p) then p fi

%p end proc:

%p map(f, [$1..4^4]); # _Robert Israel_, Dec 18 2018

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

%o (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

%Y Cf. A000040, A000217, A004022, A038603.

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

%K base,easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Nov 15 2005

%E Corrected by _Ray Chandler_, Nov 19 2005