A104247 Primes that are the sum of digits of the first k primes for some k.

2, 5, 17, 19, 23, 31, 41, 61, 71, 83, 181, 269, 389, 419, 449, 631, 683, 727, 743, 809, 929, 1039, 1061, 1069, 1091, 1277, 1381, 1481, 1567, 1613, 1747, 1873, 1951, 1993, 2039, 2129, 2281, 2297, 2339, 2381, 2549, 2579

Offset: 1

Author

Zak Seidov, Feb 26 2005

Keywords

• nonn
• base

Examples

			a(4)=19 because A058049(4)= 5 and sum of digits of the first 5 primes, 2+3+5+7+(1+1)=19 is prime.
		

Links

• M. F. Hasler, Table of n, a(n) for n = 1..1000

Crossrefs

Corresponding n's: A058049. Primes: A000040, sum of digits of primes: A007605.

Cf. A051351, A075544.

Programs

Python

from sympy import isprime, nextprime
def sd(n): return sum(map(int, str(n)))
def aupto(limit):
    alst, k, p, s = [], 1, 2, 2
    while s <= limit:
        if isprime(s): alst.append(s)
        k += 1; p = nextprime(p); s += sd(p)
    return alst
print(aupto(2579)) # Michael S. Branicky, Jul 18 2021

Formula

a(n) = A007605(1) + ... + A007605(A058049(n)).