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A347702 Prime numbers that give a remainder of 1 when divided by the sum of their digits. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

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

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: A240624 A032502 A209871 * A167794 A019336 A104070

Adjacent sequences:  A347699 A347700 A347701 * A347703 A347704 A347705

KEYWORD

nonn,base

AUTHOR

Burak Muslu, Sep 10 2021

STATUS

approved

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Last modified January 25 09:50 EST 2022. Contains 350565 sequences. (Running on oeis4.)