|
|
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
|
|
|
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
|
|
|
KEYWORD
|
base,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|