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

Author

Burak Muslu, Sep 10 2021

Keywords

• nonn
• base

Examples

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

Links

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

Crossrefs

Cf. A000040, A007605, A136251.

Subsequence of A209871.

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

Programs

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 *)

PARI

isok(p) = isprime(p) && ((p % sumdigits(p)) == 1); \\ Michel Marcus, Sep 10 2021

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