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

23, 61, 1123, 1231, 1321, 2111, 2131, 11261, 11621, 12113, 13121, 15121, 19121, 21911, 22511, 27211, 61211, 116113, 131231, 312161, 611113, 1111211, 1111213, 1111361, 1112611, 1123151, 1411411, 1612111, 2111411, 2121131, 3112111

Offset: 1

Author

Joseph L. Pe, Jan 09 2004

Keywords

• base
• nonn

Comments

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"?

See Prime Puzzle 251 link for several arguments that 23 is the only pointer prime not containing digit "1".

Examples

			23 + product of digits of 23 = 29, which is the next prime after 23. Hence 23 belongs to the sequence.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..4354 (terms < 10^19)
• Carlos Rivera's Prime Puzzles and Problems Connection, Puzzle 251, Pointer primes

Crossrefs

Cf. A091628, A091629, A091630, A091631, A091632.

Programs

Mathematica

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