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A087339 Numbers k such that both the sum of the digits of k and 1 plus the product of its digits are primes. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A137904 A175414 A059192 * A216213 A160948 A299973

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

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Last modified March 25 07:12 EDT 2019. Contains 321468 sequences. (Running on oeis4.)