A236513 The n-th prime with n 1-bits in its binary expansion.

2, 5, 13, 53, 79, 373, 379, 983, 1783, 6007, 7151, 21503, 31231, 98207, 129919, 259967, 507839, 1564159, 1830911, 4193263, 8355583, 25157567, 33288191, 92274671, 134180863, 394264447, 536838139, 1072693243, 2145382399, 6442188791, 8522825599, 17179836413

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..1014

Example

Primes p such that
A000120(p) = 1: 2;
A000120(p) = 2: 3, 5, 17, 257,...
A000120(p) = 3: 7, 11, 13, 19, 37, 41,...
A000120(p) = 4: 23, 29, 43, 53, 71, 83, 89,...
A000120(p) = 5: 31, 47, 59, 61, 79, 103, 107, 109,...
A000120(p) = 6: 311, 317, 347, 349, 359, 373,...

Mathematica

nn = 20; t = Table[-n + 1, {n, nn}]; p = 1; While[Min[t] <= 0, p = NextPrime[p]; b = Total[IntegerDigits[p, 2]]; If[b <= nn, If[t[[b]] < 0, t[[b]]++, If[t[[b]] == 0, t[[b]] = p]]]]; t (* T. D. Noe, Jan 27 2014 *)

Prog

(PARI) lista(nn) = {prm = primes(5000000); for (n = 1, nn, ltp = select(p->hammingweight(p)== n, prm); print1(ltp[n], ", "); ); } \\ Michel Marcus, Jan 27 2014
(Python)
from itertools import combinations
from sympy import isprime
def A236513(n):
    l, k, c = n-1, 2**n, 0
    while True:
        for d in combinations(range(l-1, -1, -1), l-n+1):
            m = k-1 - sum(2**(e) for e in d)
            if isprime(m):
                c += 1
                if c == n:
                    return m
        l += 1
        k *= 2 # Chai Wah Wu, Sep 02 2021

Crossrefs

Cf. A061712 (least prime having n ones in binary).

Sequence in context: A353719 A353722 A105905 * A214853 A075738 A076999

Adjacent sequences: A236510 A236511 A236512 * A236514 A236515 A236516

Keyword

nonn,easy,base

Author

Irina Gerasimova, Jan 27 2014

Extensions

a(24)-a(32) from Giovanni Resta, Feb 04 2014

Status

approved