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%I #6 Apr 15 2021 23:04:08
%S 4,15,85,619,4800,39266,332276,2880818,25423985,227527467
%N The number of primes less than 10^n whose digital root (A038194) is also prime.
%e 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}.
%t c = 0; k = 1; Do[ While[ k < 10^n, If[ PrimeQ[k] && PrimeQ[ Mod[k, 9]], c++ ]; k++ ]; Print[c], {n, 1, 8}]
%o (Python)
%o # use primerange (slower) vs. sieve.primerange (>> memory) for larger terms
%o from sympy import isprime, sieve
%o def afind(terms):
%o s = 0
%o for n in range(1, terms+1):
%o s += sum(isprime(p%9) for p in sieve.primerange(10**(n-1), 10**n))
%o print(s, end=", ")
%o afind(7) # _Michael S. Branicky_, Apr 15 2021
%Y The primes are in A078403, their digital roots are in A078400.
%K base,nonn
%O 1,1
%A _Robert G. Wilson v_, Dec 27 2002
%E a(9)-a(10) from _Michael S. Branicky_, Apr 15 2021
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