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%I #26 Mar 05 2024 15:08:42
%S 11,13,17,41,43,97,101,131,157,181,233,239,271,311,353,401,421,491,
%T 521,541,599,617,631,647,673,743,811,859,953,1021,1031,1051,1093,1171,
%U 1201,1249,1259,1301,1303,1327,1373,1531,1601,1621,1801,1871,2029,2111,2129,2161
%N Prime numbers that give a remainder of 1 when divided by the sum of their digits.
%H Robert Israel, <a href="/A347702/b347702.txt">Table of n, a(n) for n = 1..10000</a>
%e 97 is a term since its sum of digits is 9+7 = 16, and 97 mod 16 = 1.
%p select(t -> isprime(t) and t mod convert(convert(t,base,10),`+`) = 1, [seq(i,i=3..10000,2)]); # _Robert Israel_, Mar 05 2024
%t Select[Range[2000], PrimeQ[#] && Mod[#, Plus @@ IntegerDigits[#]] == 1 &] (* _Amiram Eldar_, Sep 10 2021 *)
%o (Python)
%o from sympy import primerange
%o def ok(p): return p%sum(map(int, str(p))) == 1
%o print(list(filter(ok, primerange(1, 2130)))) # _Michael S. Branicky_, Sep 10 2021
%o (PARI) isok(p) = isprime(p) && ((p % sumdigits(p)) == 1); \\ _Michel Marcus_, Sep 10 2021
%Y Cf. A000040, A007605, A136251.
%Y Subsequence of A209871.
%Y A259866 \ {31}, and the primes associated with A056804 \ {1, 2} and A056797 are subsequences.
%K nonn,base
%O 1,1
%A _Burak Muslu_, Sep 10 2021
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