A134873 Primes p with the property that the sum of the digits of the product of the digits of p is also a prime number.

2, 3, 5, 7, 13, 17, 31, 37, 43, 71, 73, 113, 127, 131, 137, 151, 173, 211, 223, 257, 271, 277, 281, 311, 317, 431, 457, 523, 541, 547, 557, 577, 727, 757, 821, 853, 1117, 1151, 1171, 1187, 1217, 1223, 1277, 1427, 1451, 1481, 1511, 1523

Offset

1,1

Links

Erich Leistenschneider, Table of n, a(n) for n = 1..4095

Erich Lestenschneider's Article about this sequence (in Portuguese).

Erich Leistenschneider, Program used to generate the sequence (Linux)

Erich Leistenschneider, First 4095 numbers of the sequence

Example

2531 is a member of this sequence because it is a prime number and the product of its digits is 2*5*3*1 = 30 and the sum of the digits of this result is 3+0 = 3, which is also a prime number.

Maple

a:=proc(n) local dn, pr, dpr: dn:=convert(n, base, 10): pr:=mul(dn[i], i=1..nops(dn)): dpr:=convert(pr, base, 10): if isprime(n)=true and isprime(add(dpr[j], j= 1..nops(dpr)))=true then n else end if end proc: seq(a(n), n=1..1600); # Emeric Deutsch, Mar 01 2008

Mathematica

Select[Prime[Range[300]], PrimeQ[Total[IntegerDigits[Times@@ IntegerDigits[#]]]]&] (* Harvey P. Dale, Dec 15 2011 *)

Prog

(PARI) isok(p) = isprime(p) && isprime(sumdigits(vecprod(digits(p)))); \\ Michel Marcus, Jan 16 2019

Crossrefs

Subsequence of A038618 (zeroless primes).

Sequence in context: A009571 A087520 A117159 * A172979 A118724 A055387

Adjacent sequences: A134870 A134871 A134872 * A134874 A134875 A134876

Keyword

nonn,base

Author

Erich Leistenschneider (el(AT)erichl.net), Feb 01 2008

Status

approved