A078403 Primes whose digital root (A038194) is prime.

2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 59, 61, 79, 83, 97, 101, 113, 131, 137, 149, 151, 167, 173, 191, 223, 227, 239, 241, 257, 263, 277, 281, 293, 311, 313, 317, 331, 347, 349, 353, 367, 383, 389, 401, 419, 421, 439, 443, 457, 461, 479, 491, 509, 547, 563, 569

Offset: 1

Author

N. J. A. Sloane, Dec 26 2002

Keywords

• base
• easy
• nonn

Comments

Union of A061238, A061240, A061241 and 3. - Ya-Ping Lu, Jan 03 2024

Examples

			59 is a term because 5+9=14, giving (final) iterated sum 1+4=5 and 5 is prime.
		

Crossrefs

Cf. A038194, A061238, A061240, A061241, A070027, A078400.

Programs

Mathematica

Select[ Range[580], PrimeQ[ # ] && PrimeQ[Mod[ #, 9]] &]
Select[Prime[Range[200]],PrimeQ[Mod[#,9]]&] (* Harvey P. Dale, Aug 20 2017 *)

PARI

forprime(p=2,997,if(isprime(p%9),print1(p,",")))

Python

from sympy import isprime, primerange; [print(p, end = ', ') for p in primerange(2, 570) if isprime(p%9)] # Ya-Ping Lu, Jan 03 2024

Formula

a(n) ~ 2n log n. - Charles R Greathouse IV, May 14 2025

Extensions

Extended by Robert G. Wilson v, Klaus Brockhaus and Rick L. Shepherd, Dec 27 2002