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A073902
Number of n-digit primes with digit sum n.
0
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
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
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