A353197 Numbers k such that k + s + k*s is prime, where s is the sum of digits of k.

1, 14, 29, 32, 38, 41, 56, 71, 89, 95, 107, 113, 119, 155, 164, 173, 185, 203, 212, 236, 251, 263, 275, 278, 290, 293, 299, 305, 311, 326, 344, 371, 377, 395, 401, 416, 419, 437, 467, 470, 473, 479, 485, 497, 509, 524, 527, 539, 569, 584, 587, 593, 611, 623, 635, 641, 659, 665, 671, 674, 692, 701

Offset

1,2

Comments

Except for 1, all terms == 2 (mod 3).

Links

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

Example

a(3) = 29 is a term because its sum of digits is 2+9 = 11 and 29 + 11 + 29*11 = 359 is prime.

Maple

f:= proc(n) local s, t;
  s:= convert(convert(n, base, 10), `+`);
  n+s+s*n;
end proc:
select(t -> isprime(f(t)), [1, seq(i, i=2..10000, 3)]);

Prog

(Python)
from sympy import isprime
def ok(n): s = sum(map(int, str(n))); return isprime(n + s + n*s)
print([k for k in range(702) if ok(k)]) # Michael S. Branicky, Apr 29 2022

Crossrefs

Cf. A007953.

Sequence in context: A305662 A174070 A045527 * A306212 A041384 A041382

Adjacent sequences: A353194 A353195 A353196 * A353198 A353199 A353200

Keyword

nonn,base

Author

Robert Israel, Apr 29 2022

Status

approved