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Base 7 sum of digits of prime(n).
3

%I #23 Mar 04 2023 04:26:50

%S 2,3,5,1,5,7,5,7,5,5,7,7,11,7,11,5,5,7,7,5,7,7,11,11,13,5,7,5,7,5,7,

%T 11,11,13,5,7,7,7,11,11,11,13,11,13,5,7,7,13,11,13,11,11,13,11,11,11,

%U 11,13,13,11,13,17,13,11,13,11,13,13,5,7,5,5,7,7

%N Base 7 sum of digits of prime(n).

%C a(n) is the rank of prime(n) in the base-7 dominance order on the natural numbers.

%H Vincenzo Librandi, <a href="/A239693/b239693.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) = A053828(A000040(n)).

%e The fifth prime is 11, 11 in base 7 is (1,4) so a(5)=1+4=5.

%t Table[Plus @@ IntegerDigits[Prime[n], 7], {n, 1, 100}] (* _Vincenzo Librandi_, Mar 25 2014 *)

%o (Sage) [sum(i.digits(base=7)) for i in primes_first_n(200)]

%o (Magma) [&+Intseq(NthPrime(n),7): n in [1..100]]; // _Vincenzo Librandi_, Mar 25 2014

%o (PARI) a(n) = sumdigits(prime(n), 7); \\ _Michel Marcus_, Mar 04 2023

%Y Cf. A007605, A014499, A053828, A239690, A239691, A239692.

%K nonn,base

%O 1,1

%A _Tom Edgar_, Mar 24 2014