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A014499 Number of 1's in binary representation of n-th prime. 44
1, 2, 2, 3, 3, 3, 2, 3, 4, 4, 5, 3, 3, 4, 5, 4, 5, 5, 3, 4, 3, 5, 4, 4, 3, 4, 5, 5, 5, 4, 7, 3, 3, 4, 4, 5, 5, 4, 5, 5, 5, 5, 7, 3, 4, 5, 5, 7, 5, 5, 5, 7, 5, 7, 2, 4, 4, 5, 4, 4, 5, 4, 5, 6, 5, 6, 5, 4, 6, 6, 4, 6, 7, 6, 7, 8, 4, 5, 4, 5, 5, 5, 7, 5, 7, 7, 4, 5, 6, 7, 6, 8, 7, 7, 7, 8, 8, 3, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is the rank of prime(n) in the base-2 dominance order on the natural numbers. - Tom Edgar, Mar 25 2014

LINKS

T. D. Noe, 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.

Christian Elsholtz, Almost all primes have a multiple of small Hamming weight, arXiv:1602.05974 [math.NT], 2016.

Index entries for sequences related to binary expansion of n

FORMULA

a(n) = A000120(A000040(n)).

a(A049084(A061712(n))) = n. - Reinhard Zumkeller, Feb 10 2013

a(n) = [x^prime(n)] (1/(1 - x))*Sum_{k>=0} x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Mar 27 2018

MATHEMATICA

f[n_] := Plus @@ IntegerDigits[n, 2]; lst = {}; Do[p = Prime[n];

AppendTo[lst, f[p]], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 10 2009 *)

Table[Plus @@ IntegerDigits[Prime[n], 2], {n, 1, 100}] (* Vincenzo Librandi, Mar 25 2014 *)

PROG

(PARI) A014499(n)=norml2(binary(prime(n))) \\ M. F. Hasler, Nov 20 2009

(Haskell)

a014499 = a000120 . a000040 -- Reinhard Zumkeller, Feb 10 2013

(Magma) [&+Intseq(NthPrime(n), 2): n in [1..100] ]; // Vincenzo Librandi, Mar 25 2014

(Sage) [sum(i.digits(base=2)) for i in primes_first_n(200)] # Tom Edgar, Mar 25 2014

CROSSREFS

Cf. A035103, A035100, A004676, A090455.

Cf. A027697, A027699

Cf. A180024. - Reinhard Zumkeller, Aug 08 2010

Cf. A072084.

Sequence in context: A194883 A328404 A175453 * A055778 A348772 A106482

Adjacent sequences: A014496 A014497 A014498 * A014500 A014501 A014502

KEYWORD

nonn,base,easy

AUTHOR

Ingemar Assarsjo (ingemar(AT)binomen.se)

STATUS

approved

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Last modified November 29 04:45 EST 2022. Contains 358422 sequences. (Running on oeis4.)