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Numbers n such that sum of digits and product of digits are both prime.
2

%I #12 Nov 09 2021 05:49:33

%S 2,3,5,7,12,21,113,115,131,151,311,511,1112,1121,1211,2111,11113,

%T 11117,11131,11171,11311,11711,13111,17111,31111,71111,111112,111121,

%U 111211,112111,121111,211111,1111115,1111117,1111151,1111171,1111511,1111711

%N Numbers n such that sum of digits and product of digits are both prime.

%C One digit must be 2, 3, 5, or 7 and every other digit must be 1. If k is in the sequence, then so is every permutation of the digits of k. - _Sean A. Irvine_, Nov 08 2021

%H Sean A. Irvine, <a href="/A052430/b052430.txt">Table of n, a(n) for n = 1..994</a>

%e a(7)=115 because 1+1+5=7 which is prime and 1*1*5=5 which is prime

%t okQ[n_]:=Module[{idn=IntegerDigits[n]},PrimeQ[Total[idn]]&&PrimeQ[Times@@idn]]

%t Select[Range[1500000],okQ] (* _Harvey P. Dale_, Dec 15 2010 *)

%Y Cf. A000040, A028834, A028842.

%K base,nonn

%O 1,1

%A _Henry Bottomley_, Mar 14 2000