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

Author

Tom Edgar, Mar 24 2014

Keywords

• nonn
• base
• hear

Comments

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

Examples

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

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, A053737, A239619.

Cf. A000040, A007090.

Programs

Haskell

a239690 = a053737 . a000040  -- Reinhard Zumkeller, Mar 20 2015

Magma

[&+Intseq(NthPrime(n),4): n in [1..100]]; // Vincenzo Librandi, Mar 25 2014

Mathematica

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

Sage

[sum(i.digits(base=4)) for i in primes_first_n(200)]

Formula

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