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

1,1

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

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 *)

Crossrefs

Cf. A087340.

Sequence in context: A175414 A359220 A059192 * A345922 A216213 A160948

Adjacent sequences: A087336 A087337 A087338 * A087340 A087341 A087342

Keyword

base,nonn

Author

Amarnath Murthy, Sep 06 2003

Extensions

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

Status

approved