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 A046713 Multiplicative and additive primes: primes where the product and sum of digits are also prime. 6
 2, 3, 5, 7, 113, 131, 151, 311, 2111, 11113, 11117, 11131, 11171, 11311, 111121, 111211, 112111, 1111151, 1111711, 1117111, 1171111, 111111113, 111111131, 111113111, 115111111, 131111111, 1111111121, 1111211111, 1121111111, 11111111113, 11111111131, 11113111111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Any term of this sequence has one prime digit and all other digits are 1. - Sean A. Irvine, Apr 17 2021 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 MATHEMATICA d[n_]:=IntegerDigits[n]; t={}; Do[p=Prime[n]; If[PrimeQ[Plus@@(x=d[p])]&&PrimeQ[Times@@x], AppendTo[t, p]], {n, 2*10^5}]; t (* Jayanta Basu, May 18 2013 *) Select[Prime[Range[5033*10^5]], AllTrue[{Total[IntegerDigits[ #]], Times@@ IntegerDigits[ #]}, PrimeQ]&] (* or -- much faster *) Select[Union[ Flatten[ Table[FromDigits/@Permutations[PadRight[{p}, n, 1]], {p, {2, 3, 5, 7}}, {n, 11}]]], AllTrue[{#, Total[ IntegerDigits[#]], Times@@ IntegerDigits[ #]}, PrimeQ]&] (* Harvey P. Dale, Feb 28 2022 *) CROSSREFS Intersection of A028834, A028842, and A000040. Intersection of A046703 and A046704. Sequence in context: A205529 A006341 A086107 * A119835 A076609 A117059 Adjacent sequences:  A046710 A046711 A046712 * A046714 A046715 A046716 KEYWORD nonn,base AUTHOR EXTENSIONS More terms from Harvey P. Dale, Aug 23 2000 Corrected by Jud McCranie, Jan 03 2001 Edited by Charles R Greathouse IV, Aug 02 2010 STATUS approved

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Last modified August 13 07:13 EDT 2022. Contains 356078 sequences. (Running on oeis4.)