A066195 -id:A066195 - cp's OEIS frontend

A236695 The n-th prime with n 0-bits in its binary expansion.

2, 43, 41, 139, 269, 773, 1049, 2309, 4357, 8737, 16673, 34819, 66569, 139393, 279553, 589829, 1051649, 2621569, 4260097, 9437189, 17039489, 33817601, 67649537, 167903233, 269484097, 545260033, 1074267137, 2155872769, 4311760897, 12884901893, 17184063521

Offset: 1

Irina Gerasimova, Jan 30 2014

			Primes p(k) such that
A035103(p(k)) = 0: 3, 7, 31, 127, 8191,...
A035103(p(k)) = 1: 2, 5, 11, 13, 23, 29,...
A035103(p(k)) = 2: 19, 43, 53, 79, 103, 107,...
A035103(p(k)) = 3: 17, 37, 41, 71, 83, 89, 101,...
A035103(p(k)) = 4: 67, 73, 97, 139, 149, 163,...
A035103(p(k)) = 5: 131, 137, 193, 263, 269, 277,...

Alois P. Heinz, Table of n, a(n) for n = 1..500 (first 40 terms from Charles R Greathouse IV)

Cf. A066195 (least prime having n zeros in binary), A236513 (the n-th prime with n 1-bits in its binary expansion).

nz(n)=#binary(n)-hammingweight(n)
a(n)=my(k=n);forprime(p=2,,if(nz(p)==n&&k--==0,return(p))) \\ Charles R Greathouse IV, Feb 04 2014

New name from Ralf Stephan and Charles R Greathouse IV, Feb 04 2014
a(14)-a(27) from Charles R Greathouse IV, Feb 04 2014
a(28)-a(31) from Giovanni Resta, Feb 04 2014

A102566 a(n) = {minimal k such that f^k(prime(n)) = 1} where f(m) = (m+1)/2^r, 2^r is the highest power of two dividing m+1.

Original entry on oeis.org

2, 1, 2, 1, 2, 2, 4, 3, 2, 2, 1, 4, 4, 3, 2, 3, 2, 2, 5, 4, 5, 3, 4, 4, 5, 4, 3, 3, 3, 4, 1, 6, 6, 5, 5, 4, 4, 5, 4, 4, 4, 4, 2, 6, 5, 4, 4, 2, 4, 4, 4, 2, 4, 2, 8, 6, 6, 5, 6, 6, 5, 6, 5, 4, 5, 4, 5, 6, 4, 4, 6, 4, 3, 4, 3, 2, 6, 5, 6, 5, 5, 5, 3, 5, 3, 3, 6, 5, 4, 3, 4, 2, 3, 3, 3, 2, 2, 8, 7, 6, 7, 6, 6, 6, 5

Offset: 1

Yasutoshi Kohmoto, Feb 25 2005

A066195(n+1) is the prime corresponding to the first n in this sequence. - David Wasserman, Apr 08 2008

			f(f(f(f(17)))) = 1, prime(7) = 17, so a(7) = 4.
prime(16) = 53 = (2*27-1) = (2*(2^2*7-1)-1) = (2*(2^2*(2^3*1-1)-1)-1), has 3 levels, so a(16) = 3.

Cf. A023416, A035103, A066195.

f(n) = (n+1)/2^(valuation(n+1, 2));
a(n) = {my(k = 1, p = prime(n)); while((q=f(p)) != 1, k++; p = q); k;} \\ Michel Marcus, Nov 20 2016

a(n) = my(p=prime(n)); 2 + logint(p, 2) - hammingweight(p); \\ Kevin Ryde, Nov 06 2023

a(n) = A023416(prime(n)) + 1. - David Wasserman, Apr 08 2008

a(n) = A035103(n) + 1. - Filip Zaludek, Nov 19 2016

More terms from David Wasserman, Apr 08 2008

cp's OEIS Frontend

A236695 The n-th prime with n 0-bits in its binary expansion.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Extensions

A102566 a(n) = {minimal k such that f^k(prime(n)) = 1} where f(m) = (m+1)/2^r, 2^r is the highest power of two dividing m+1.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

PARI

Formula

Extensions