A079155 The number of primes less than 10^n whose digital root (A038194) is also prime.

4, 15, 85, 619, 4800, 39266, 332276, 2880818, 25423985, 227527467

Offset: 1

Author

Robert G. Wilson v, Dec 27 2002

Keywords

• base
• nonn

Examples

			a(2) = 15 because the only primes less than 100 whose have digital roots are also prime are {2,3,5,7,11,23,29,41,43,47,59,61,79,83,97}.
		

Crossrefs

The primes are in A078403, their digital roots are in A078400.

Programs

Mathematica

c = 0; k = 1; Do[ While[ k < 10^n, If[ PrimeQ[k] && PrimeQ[ Mod[k, 9]], c++ ]; k++ ]; Print[c], {n, 1, 8}]

Python

# use primerange (slower) vs. sieve.primerange (>> memory) for larger terms
from sympy import isprime, sieve
def afind(terms):
  s = 0
  for n in range(1, terms+1):
    s += sum(isprime(p%9) for p in sieve.primerange(10**(n-1), 10**n))
    print(s, end=", ")
afind(7) # Michael S. Branicky, Apr 15 2021

Extensions

a(9)-a(10) from Michael S. Branicky, Apr 15 2021