A239694 Base 8 sum of digits of prime(n).

2, 3, 5, 7, 4, 6, 3, 5, 9, 8, 10, 9, 6, 8, 12, 11, 10, 12, 4, 8, 3, 9, 6, 5, 6, 10, 12, 9, 11, 8, 15, 5, 4, 6, 9, 11, 10, 9, 13, 12, 11, 13, 16, 4, 8, 10, 8, 13, 10, 12, 9, 15, 10, 13, 5, 11, 10, 12, 11, 8, 10, 13, 13, 17, 12, 16, 9, 8, 11, 13, 10, 16, 17, 16

Offset: 1

Author

Tom Edgar, Mar 24 2014

Keywords

• nonn
• base

Comments

a(n) is the rank of prime(n) in the base-8 dominance order on the natural numbers.

Examples

			The sixth prime is 13, 13 in base 8 is (1,5) so a(6)=1+5=6.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Tyler Ball and Daniel Juda, Dominance over N, Rose-Hulman Undergraduate Mathematics Journal, Vol. 13, No. 2, Fall 2013.

Crossrefs

Cf. A007605, A014499, A053829, A239690, A239691, A239692, A239693.

Programs

Magma

[&+Intseq(NthPrime(n),8): n in [1..100]]; // Vincenzo Librandi, Mar 25 2014

Mathematica

Table[Plus @@ IntegerDigits[Prime[n], 8], {n, 1, 100}] (* Vincenzo Librandi, Mar 25 2014 *)

PARI

a(n) = sumdigits(prime(n), 8); \\ Michel Marcus, Mar 04 2023

Sage

[sum(i.digits(base=8)) for i in primes_first_n(200)]

Formula

a(n) = A053829(A000040(n)).