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

1,1

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".

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

Example

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

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

Crossrefs

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

Sequence in context: A355985 A232235 A107692 * A304896 A316578 A323220

Adjacent sequences: A089820 A089821 A089822 * A089824 A089825 A089826

Keyword

base,nonn

Author

Joseph L. Pe, Jan 09 2004

Status

approved