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A239690 Base 4 sum of digits of prime(n). 7
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 1 11:38 EDT 2022. Contains 357147 sequences. (Running on oeis4.)