A062341 Primes whose sum of digits is 5.

5, 23, 41, 113, 131, 311, 401, 1013, 1031, 1103, 1301, 2003, 2111, 3011, 4001, 10103, 10211, 10301, 11003, 12011, 12101, 13001, 20021, 20201, 21011, 21101, 30011, 100103, 101021, 101111, 102101, 103001, 120011, 121001, 200003, 200201, 201011, 201101, 202001

Offset: 1

Author

Amarnath Murthy, Jun 21 2001

Keywords

• nonn
• base
• easy

Examples

			1301 belongs to the sequence since it is a prime with sum of digits = 5.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..14312 (first 100 terms from Harvey P. Dale)

Crossrefs

Cf. A000040 (primes), A007953 (sum of digits), A052219 (digit sum = 5).

Cf. A062339 (same for digit sum s = 4), A062337 (s = 7), and others listed in A244918 (s = 68).

Subsequence of A062340 (primes with sum of digits divisible by 5).

Programs

Magma

[p: p in PrimesUpTo(250000) | &+Intseq(p) eq 5]; // Vincenzo Librandi, Jul 08 2014

Maple

T:= n-> `if`(n=1, 5, sort(select(isprime, [seq(seq(seq(
    10^(n-1)+1+10^i+10^j+10^k, k=1..j), j=1..i), i=1..n-1),
    seq(10^(n-1)+3+10^i, i=1..n-1)]))[]):
seq(T(n), n=1..8);  # Alois P. Heinz, Dec 28 2015

Mathematica

Select[Prime[Range[20000]],Total[IntegerDigits[#]]==5&] (* Harvey P. Dale, Nov 24 2013 *)

PARI

\\ From M. F. Hasler, Mar 09 2022: (Start)
select( {is_A062341(p,s=5)=sumdigits(p)==s&&isprime(p)}, primes([1,10^6])) \\ 2nd optional parameter for similar sequences with other digit sums.
A062341_upto_length(L,s=5,a=List(),u=[10^k|k<-[0..L-1]])={forvec(d=[[1,L]|i<-[1..s]], isprime(p=vecsum(vecextract(u,d))) && listput(a,p),1); Set(a)} \\ (End)

Python

from sympy import primerange as primes
def ok(p): return sum(map(int, str(p))) == 5
print(list(filter(ok, primes(1, 202002)))) # Michael S. Branicky, May 23 2021

Formula

Intersection of A000040 (primes) with A052219 (digit sum 5). - M. F. Hasler, Mar 09 2022

Extensions

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jul 06 2001