A225864 Composite numbers for which both sum and product of digits are primes.

12, 21, 115, 511, 1112, 1121, 1211, 11711, 13111, 17111, 31111, 71111, 111112, 121111, 211111, 1111115, 1111117, 1111171, 1111511, 1115111, 1151111, 1511111, 1711111, 5111111, 7111111, 111111115, 111111151, 111111311, 111111511, 111115111, 111131111, 111151111

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Mathematica

d[n_] := IntegerDigits[n]; t={}; Do[If[!PrimeQ[n] && PrimeQ[Plus@@(x=d[n])] && PrimeQ[Times@@x], AppendTo[t, n]], {n, 2*10^6}]; t
Select[Range[72*10^5], CompositeQ[#]&&AllTrue[{Total[IntegerDigits[#]], Times@@ IntegerDigits[ #]}, PrimeQ]&] (* The program generates the first 25 terms of the sequence. *) (* Harvey P. Dale, May 24 2024 *)

Prog

(Python)
from __future__ import division
from sympy import isprime
A225864_list = []
for l in range(1, 20):
    plist, q = [p for p in [2, 3, 5, 7] if isprime(l-1+p)], (10**l-1)//9
    for i in range(l):
        for p in plist:
            r = q+(p-1)*10**i
            if not isprime(r):
                A225864_list.append(r) # Chai Wah Wu, Aug 15 2017

Crossrefs

Cf. A046713, A225863.

Sequence in context: A201015 A044005 A321771 * A134514 A030299 A352991

Adjacent sequences: A225861 A225862 A225863 * A225865 A225866 A225867

Keyword

nonn,base

Author

Jayanta Basu, May 18 2013

Extensions

Extended by T. D. Noe, May 18 2013

Status

approved