A225303 Primes of the form p + (product of digits of p), where p is a prime.

29, 47, 67, 101, 103, 107, 109, 181, 251, 293, 307, 331, 347, 401, 409, 431, 443, 457, 491, 503, 509, 547, 593, 601, 607, 631, 653, 659, 673, 701, 709, 743, 809, 823, 827, 839, 907, 929, 971, 977, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091

Offset: 1

Author

Jayanta Basu, May 05 2013

Keywords

• nonn
• base

Comments

Primes generated by A157677.

Examples

			29 is in the list since 29 = 23 + (2*3).
		

Links

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

Crossrefs

Cf. A157677.

Programs

Maple

f:= proc(n) local L,v;
  if not isprime(n) then return NULL fi;
  L:= convert(n,base,10);
  if member(0,L) then return n fi;
  v:= n + convert(L,`*`);
  if isprime(v) then v else NULL fi
end proc:
N:= 2000: # to get all terms <= N
S:= {}:
for n from 3 by 2 to N do
  v:= f(n);
  if v <> NULL and v <= N then S:= S union {v} fi;
od:
sort(convert(S,list));# Robert Israel, Jun 25 2019

Mathematica

Sort[DeleteDuplicates[Select[Table[p=Prime[n]; p+Times@@IntegerDigits[p], {n,175}],PrimeQ]]]
Select[Table[p+Times@@IntegerDigits[p],{p,Prime[Range[ 200]]}], PrimeQ]// Union (* Harvey P. Dale, Sep 21 2019 *)

Extensions

1049,1051,1061,1063,1069 and 1087 inserted by Robert Israel, Jun 25 2019