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Base 6 sum of digits of prime(n).
4

%I #22 Mar 04 2023 04:26:42

%S 2,3,5,2,6,3,7,4,8,9,6,2,6,3,7,8,9,6,7,11,3,4,8,9,7,11,8,12,4,8,7,11,

%T 12,9,9,6,7,8,12,13,14,6,11,8,12,9,11,3,7,4,8,9,6,11,7,8,9,6,7,11,8,8,

%U 7,11,8,12,6,7,12,9,13,14,7,8,9,13,14,7,11,9

%N Base 6 sum of digits of prime(n).

%C a(n) is the rank of prime(n) in the base-6 dominance order on the natural numbers.

%H Vincenzo Librandi, <a href="/A239692/b239692.txt">Table of n, a(n) for n = 1..10000</a>

%H Tyler Ball and Daniel Juda, <a href="https://scholar.rose-hulman.edu/rhumj/vol14/iss2/2">Dominance over N</a>, Rose-Hulman Undergraduate Mathematics Journal, Vol. 13, No. 2, Fall 2013.

%F a(n) = A053827(A000040(n)).

%e The sixth prime is 13, 13 in base 6 is (2,1) so a(6)=2+1=3.

%t Table[Plus @@ IntegerDigits[Prime[n], 6], {n, 1, 100}] (* _Vincenzo Librandi_, Mar 25 2014 *)

%o (Sage) [sum(i.digits(base=6)) for i in primes_first_n(200)]

%o (Magma) [&+Intseq(NthPrime(n),6): n in [1..100]]; // _Vincenzo Librandi_, Mar 25 2014

%o (PARI) a(n) = sumdigits(prime(n), 6); \\ _Michel Marcus_, Mar 04 2023

%Y Cf. A007605, A014499, A053827, A239690, A239691.

%K nonn,base

%O 1,1

%A _Tom Edgar_, Mar 24 2014