A087339 Numbers k such that both the sum of the digits of k and 1 plus the product of its digits are primes.

2, 11, 12, 14, 16, 21, 23, 25, 29, 32, 34, 41, 43, 47, 49, 52, 56, 58, 61, 65, 67, 74, 76, 85, 89, 92, 94, 98, 111, 122, 128, 166, 182, 212, 218, 221, 223, 227, 229, 232, 236, 245, 254, 256, 263, 265, 269, 272, 278, 281, 287, 292, 296, 322, 326, 346, 362, 364, 388

Offset: 1

Author

Amarnath Murthy, Sep 06 2003

Keywords

• base
• nonn

Comments

Sequence is infinite. Proof: (10^p-1)/9 is a term if p is a prime. The sum of the digits = p and the product of digits + 1 = 2. Conjecture: There are infinitely many terms not of the form (10^p-1)/9.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A087340.

Programs

Mathematica

f[n_] := Block[{d = IntegerDigits[n]}, PrimeQ[Plus @@ d] && PrimeQ[1 + Times @@ d]]; Select[ Range[424], f[ # ] & ]
Select[Range[400],AllTrue[{Total[IntegerDigits[#]],Times @@ IntegerDigits[ #]+1}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 24 2017 *)

Extensions

More terms from Robert G. Wilson v, Sep 07 2003