A157655 Zeroless primes p such that the next prime after p can be obtained from p by adding the sum and product of the digits of p.

11411, 16111, 1112113, 1151113, 14161111, 14611111, 111115141, 111253111, 115112113, 122112311, 151151111, 211711111, 1111116211, 1121123111, 1121181311, 1211215111, 1412113111, 1416131111, 2111121511, 2111215111

Offset

1,1

Comments

If we allow a zero digit in p, we generate A089824. One could conjecture that the digit 1 must always appear in the entries of this sequence. The idea for this sequence and the description was motivated by A089823.

Links

Table of n, a(n) for n=1..20.

Cino Hilliard, Pointer primes [broken link]

Example

The digits of 11411 add up to 8. The product of the digits is 4. So 11411+8+4 = 11423, the next prime after 11411. So 11411 is in the sequence.

Mathematica

zpQ[n_]:=Module[{idn=IntegerDigits[n]}, FreeQ[idn, 0]&&NextPrime[n] == n+ Total[ idn]+Times@@idn]; Select[Prime[Range[11*10^7]], zpQ] (* Harvey P. Dale, Jan 14 2016 *)

Prog

(Other) The link has the Gcc/Gmp program that was used to generate this sequence.

Crossrefs

Cf. A089823, A089824.

Sequence in context: A185768 A082440 A083975 * A262399 A115753 A257172

Adjacent sequences: A157652 A157653 A157654 * A157656 A157657 A157658

Keyword

base,nonn

Author

Cino Hilliard, Mar 03 2009

Status

approved