A089227 Numbers k such that 1 + k*ds(k) is prime, where ds(k) is the sum of digits of k.

1, 2, 4, 6, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 28, 33, 34, 35, 38, 44, 46, 48, 50, 51, 54, 56, 59, 64, 68, 70, 71, 78, 80, 82, 84, 88, 90, 91, 92, 93, 94, 97, 98, 99, 100, 102, 104, 105, 106, 107, 109, 112, 116, 118, 123, 128, 129, 130, 136, 138, 140, 144, 145

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

10 is in the sequence because A007953(10) = 1 and 1 + 10*1 = 11 is prime.

Maple

ds:= n -> convert(convert(n, base, 10), `+`):
filter:= n -> isprime(1+n*ds(n)):
select(filter, [$1..1000]); # Robert Israel, Jun 20 2019

Mathematica

Do[k = Plus @@ IntegerDigits[n]; If[PrimeQ[n*k + 1], Print[n]], {n, 1, 100}] (* Ryan Propper *)
Select[Range[150], PrimeQ[#*Total[IntegerDigits[#]]+1]&] (* Harvey P. Dale, May 25 2024 *)

Prog

(PARI) isok(k) = isprime(1+k*sumdigits(k)); \\ Michel Marcus, Jun 20 2019
(Magma) [k:k in [1..145] | IsPrime(1+k*(&+Intseq(k, 10)))]; // Marius A. Burtea, Jun 21 2019

Crossrefs

Cf. A007953, A057147.

Sequence in context: A321805 A333412 A376150 * A204660 A275956 A109133

Adjacent sequences: A089224 A089225 A089226 * A089228 A089229 A089230

Keyword

nonn,base

Author

Yalcin Aktar, Dec 10 2003

Extensions

More terms from David Wasserman, Aug 31 2005

Status

approved