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

1,4

Comments

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

Links

Table of n, a(n) for n=1..19.

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A069710.

Sequence in context: A099733 A350259 A330989 * A144207 A016487 A370707

Adjacent sequences: A073899 A073900 A073901 * A073903 A073904 A073905

Keyword

base,nonn

Author

Amarnath Murthy, Aug 18 2002

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

Status

approved