A073902 Number of n-digit primes with digit sum n.

0, 1, 0, 4, 12, 0, 95, 212, 0, 2395, 10657, 0, 126068, 375941, 0, 4943357, 20513691, 0, 271911476

Offset: 1

Author

Amarnath Murthy, Aug 18 2002

Keywords

• base
• nonn

Comments

a(3n) = 0. - Sascha Kurz, Aug 23 2002

Examples

			a(2) = 1 because the only two-digit prime with digit sum 2 is 11. a(5) = 12: the primes are 10103, 10211, 10301, 11003, 12011, 12101, 13001, 20021, 20201, 21011, 21101, and 30011.
		

Crossrefs

Cf. A069710.

Programs

Mathematica

Table[Length[Select[Prime[Range[PrimePi[10^(n-1)]+1,PrimePi[10^n]]], Total[IntegerDigits[#]]==n&]],{n,8}] (* Harvey P. Dale, Aug 09 2011 *)

Python

from sympy import isprime
def nextsod(n, base):
    c, b, w = 0, base, 0
    while True:
        d = n%b
        if d+1 < b and c:
            return (n+1)*b**w + ((c-1)%(b-1)+1)*b**((c-1)//(b-1))-1
        c += d; n //= b; w += 1
def a(n):
    if n%3 == 0: return 0
    c, t = 0, 10**(n-1) + ((n-1)%9+1)*10**((n-1)//9)-1
    while t < 10**n:
        if isprime(t): c += 1
        t = nextsod(t, 10)
    return c
print([a(n) for n in range(1, 13)]) # Michael S. Branicky, Aug 02 2022

Extensions

More terms from Sascha Kurz, Aug 23 2002

a(4) and a(5) corrected, and example corrected, by Harvey P. Dale, Aug 09 2011

a(11) corrected and a(13)-a(15) from Donovan Johnson, Aug 10 2011

a(16)-a(18) from David Radcliffe, May 05 2015

a(19) from Michael S. Branicky, Aug 02 2022