A239690 Base 4 sum of digits of prime(n).

2, 3, 2, 4, 5, 4, 2, 4, 5, 5, 7, 4, 5, 7, 8, 5, 8, 7, 4, 5, 4, 7, 5, 5, 4, 5, 7, 8, 7, 5, 10, 5, 5, 7, 5, 7, 7, 7, 8, 8, 8, 7, 11, 4, 5, 7, 7, 10, 8, 7, 8, 11, 7, 11, 2, 5, 5, 7, 4, 5, 7, 5, 7, 8, 7, 8, 7, 4, 8, 7, 5, 8, 10, 7, 10, 11, 5, 7, 5, 7, 8, 7, 11, 7

Offset

1,1

Comments

a(n) is the rank of prime(n) in the base-4 dominance order on the natural numbers.

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.

Formula

a(n) = A053737(A000040(n)).

Example

The sixth prime is 13, 13 in base 4 is (3,1) so a(6)=3+1=4.

Mathematica

Table[Plus @@ IntegerDigits[Prime[n], 4], {n, 1, 100}] (* Vincenzo Librandi, Mar 25 2014 *)

Prog

(Sage) [sum(i.digits(base=4)) for i in primes_first_n(200)]
(Magma) [&+Intseq(NthPrime(n), 4): n in [1..100]]; // Vincenzo Librandi, Mar 25 2014
(Haskell)
a239690 = a053737 . a000040  -- Reinhard Zumkeller, Mar 20 2015

Crossrefs

Cf. A007605, A014499, A053737, A239619.

Cf. A000040, A007090.

Sequence in context: A161908 A026358 A304098 * A208460 A343934 A119465

Adjacent sequences: A239687 A239688 A239689 * A239691 A239692 A239693

Keyword

nonn,base,hear

Author

Tom Edgar, Mar 24 2014

Status

approved