cp's OEIS Frontend

A089823 Primes p such that the next prime after p can be obtained from p by adding the product of the digits of p.

%I A089823 #6 Feb 11 2014 19:05:42
%S A089823 23,61,1123,1231,1321,2111,2131,11261,11621,12113,13121,15121,19121,
%T A089823 21911,22511,27211,61211,116113,131231,312161,611113,1111211,1111213,
%U A089823 1111361,1112611,1123151,1411411,1612111,2111411,2121131,3112111
%N A089823 Primes p such that the next prime after p can be obtained from p by adding the product of the digits of p.
%C A089823 I call these primes (multiplicative) "pointer primes", in the sense that such primes p "point" to the next prime after p when the product of the digits of p is added to p. 23 is the only pointer prime < 10^7 which does not contain the digit "1". Are there other pointer primes not containing the digit "1"?
%C A089823 See Prime Puzzle 251 link for several arguments that 23 is the only pointer prime not containing digit "1".
%H A089823 Giovanni Resta, <a href="/A089823/b089823.txt">Table of n, a(n) for n = 1..4354</a> (terms < 10^19)
%H A089823 Carlos Rivera's Prime Puzzles and Problems Connection, <a href="http://www.primepuzzles.net/puzzles/puzz_251.htm">Puzzle 251, Pointer primes</a>
%e A089823 23 + product of digits of 23 = 29, which is the next prime after 23. Hence 23 belongs to the sequence.
%t A089823 r = {}; Do[p = Prime[i]; q = Prime[i + 1]; If[p + Apply[Times, IntegerDigits[p]] == q, r = Append[r, p]], {i, 1, 10^6}]; r
%Y A089823 Cf. A091628, A091629, A091630, A091631, A091632.
%K A089823 base,nonn
%O A089823 1,1
%A A089823 _Joseph L. Pe_, Jan 09 2004