[go: up one dir, main page]

login
A353197
Numbers k such that k + s + k*s is prime, where s is the sum of digits of k.
1
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
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
KEYWORD
nonn,base
AUTHOR
Robert Israel, Apr 29 2022
STATUS
approved