%I #13 May 24 2023 19:14:58
%S 11,13,17,211,233,277,367,431,457,523,541,547,587,727,743,761,853,857,
%T 1153,1223,1373,1447,1483,1531,1571,1627,1663,1733,1861,2141,2213,
%U 2251,2273,2293,2347,2383,2411,2437,2473,2521,2617,2657,2741,2833,2851,3221,3371
%N Primes p such that the sum of decimal digits of p divides the product of decimal digits of p+1 and that product is nonzero.
%H Nathaniel Johnston, <a href="/A178339/b178339.txt">Table of n, a(n) for n = 1..10000</a>
%e 2+3+3 = 8 divides 2*3*4 = 24, so 233 is a member.
%p A178339 := proc(n) option remember: local p,q: if(n=1)then return 11: fi: p:=procname(n-1): do p:=nextprime(p): q:=mul(d,d=convert(p+1,base,10)): if(q>0 and q mod add(d,d=convert(p,base,10)) = 0)then return p: fi: od: end: seq(A178339(n),n=1..47); # _Nathaniel Johnston_, May 27 2011
%t fQ[n_] := Block[{s = Plus @@ IntegerDigits@n, p = Times @@ IntegerDigits[n + 1]}, Mod[p, s] == 0 && p > 0]; Select[ Prime@ Range@ 250, fQ@# &]; Select[ Prime@ Range@ 500, fQ@# &]
%t Select[Prime[Range[500]],DigitCount[#+1,10,0]==0&&Divisible[Times@@IntegerDigits[ #+1],Total[ IntegerDigits[#]]]&] (* _Harvey P. Dale_, May 24 2023 *)
%K base,easy,nonn
%O 1,1
%A _Giovanni Teofilatto_, May 25 2010
%E Corrected and extended by _Robert G. Wilson v_, Jun 05 2010
%E Name corrected by _Nathaniel Johnston_, May 27 2011