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

Author

Cino Hilliard, Mar 03 2009

Keywords

• base
• nonn

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.

Examples

			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.
		

Links

• Cino Hilliard, Pointer primes [broken link]

Crossrefs

Cf. A089823, A089824.

Programs

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 *)