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

Author

Yalcin Aktar, Dec 10 2003

Keywords

• nonn
• base

Examples

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

Links

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

Crossrefs

Cf. A007953, A057147.

Programs

Magma

[k:k in [1..145] | IsPrime(1+k*(&+Intseq(k,10)))]; // Marius A. Burtea, Jun 21 2019

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 *)

PARI

isok(k) = isprime(1+k*sumdigits(k)); \\ Michel Marcus, Jun 20 2019

Extensions

More terms from David Wasserman, Aug 31 2005