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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. 0
11411, 16111, 1112113, 1151113, 14161111, 14611111, 111115141, 111253111, 115112113, 122112311, 151151111, 211711111, 1111116211, 1121123111, 1121181311, 1211215111, 1412113111, 1416131111, 2111121511, 2111215111 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 26 07:39 EDT 2022. Contains 354877 sequences. (Running on oeis4.)