A046713 Multiplicative and additive primes: primes where the product and sum of digits are also prime.

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

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

References

James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 113.

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

Felice Russo

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