A347702 Prime numbers that give a remainder of 1 when divided by the sum of their digits.

11, 13, 17, 41, 43, 97, 101, 131, 157, 181, 233, 239, 271, 311, 353, 401, 421, 491, 521, 541, 599, 617, 631, 647, 673, 743, 811, 859, 953, 1021, 1031, 1051, 1093, 1171, 1201, 1249, 1259, 1301, 1303, 1327, 1373, 1531, 1601, 1621, 1801, 1871, 2029, 2111, 2129, 2161

Offset

1,1

Links

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

Example

97 is a term since its sum of digits is 9+7 = 16, and 97 mod 16 = 1.

Maple

select(t -> isprime(t) and t mod convert(convert(t, base, 10), `+`) = 1, [seq(i, i=3..10000, 2)]); # Robert Israel, Mar 05 2024

Mathematica

Select[Range[2000], PrimeQ[#] && Mod[#, Plus @@ IntegerDigits[#]] == 1 &] (* Amiram Eldar, Sep 10 2021 *)

Prog

(Python)
from sympy import primerange
def ok(p): return p%sum(map(int, str(p))) == 1
print(list(filter(ok, primerange(1, 2130)))) # Michael S. Branicky, Sep 10 2021
(PARI) isok(p) = isprime(p) && ((p % sumdigits(p)) == 1); \\ Michel Marcus, Sep 10 2021

Crossrefs

Cf. A000040, A007605, A136251.

Subsequence of A209871.

A259866 \ {31}, and the primes associated with A056804 \ {1, 2} and A056797 are subsequences.

Sequence in context: A375091 A032502 A209871 * A167794 A019336 A104070

Adjacent sequences: A347699 A347700 A347701 * A347703 A347704 A347705

Keyword

nonn,base

Author

Burak Muslu, Sep 10 2021

Status

approved