A062340 Primes whose sum of digits is a multiple of 5.

5, 19, 23, 37, 41, 73, 109, 113, 127, 131, 163, 181, 271, 307, 311, 389, 401, 433, 479, 523, 541, 569, 587, 613, 631, 659, 677, 811, 839, 857, 929, 947, 983, 997, 1009, 1013, 1031, 1063, 1103, 1117, 1153, 1171, 1289, 1301, 1423, 1487, 1531, 1559, 1621, 1667

Offset: 1

Author

Amarnath Murthy, Jun 21 2001

Keywords

• nonn
• base
• easy

Examples

			569 is a prime with sum of digits = 20, hence belongs to the sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007953 (sum of digits), A227793 (sum of digits divisible by 5).

Has as subsequence A062341 (primes with sum of digits s = 5), A107579 (s = 10), A106760 (s = 20), A106763 (s = 25), A106770 (s = 35), A106773 (s = 40), A106780 (s = 50), A106783 (s = 55), A107619 (s = 65) and A181321 (s = 70).

Cf. A062340 (equivalent for 8).

Programs

Magma

[ p: p in PrimesUpTo(10000) | &+Intseq(p) mod 5 eq 0 ]; // Vincenzo Librandi, Apr 02 2011

Mathematica

Select[Prime[Range[300]],Divisible[Total[IntegerDigits[#]],5]&] (* Harvey P. Dale, Jul 06 2020 *)

PARI

select( {is_A062340(n)=sumdigits(n)%5==0&&isprime(n)}, primes([1,2000])) \\ M. F. Hasler, Mar 10 2022

Python

from sympy import primerange as primes
def ok(p): return sum(map(int, str(p)))%5 == 0
print(list(filter(ok, primes(1, 1668)))) # Michael S. Branicky, May 19 2021

Formula

Intersection of A000040 (primes) and A227793 (sum of digits in 5Z). - M. F. Hasler, Mar 10 2022

Extensions

Corrected and extended by Harvey P. Dale and Larry Reeves (larryr(AT)acm.org), Jul 04 2001