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

Author

Irina Gerasimova, Jan 27 2014

Keywords

• nonn
• easy
• base

Examples

			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,...
		

Links

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

Crossrefs

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

Programs

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 *)

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

Extensions

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