A081093 a(n) is the smallest prime such that the number of 1's in its binary expansion is equal to the n-th prime.

3, 7, 31, 127, 3583, 8191, 131071, 524287, 14680063, 1073479679, 2147483647, 266287972351, 4260607557631, 17591112302591, 246290604621823, 17996806323437567, 1152917106560335871, 2305843009213693951, 295147623704376115199, 4648579506574807007231

Offset

1,1

Comments

a(n) = Min{p: A000120(p)=A000040(n), p prime}.

If 2^(Prime[n]) - 1 is a prime number, then a(n) = 2^(Prime[n]) - 1, where Prime[n] denotes the n-th prime number. This means that every Mersenne prime arises in this sequence. - Stefan Steinerberger, Jan 22 2006

For all n with prime(n) < 300, a(n) has either prime(n) or prime(n)+1 bits. - David Wasserman, Oct 25 2006

Links

Sean A. Irvine, Table of n, a(n) for n = 1..200

Formula

a(n) = A061712(A000040(n)). - Franklin T. Adams-Watters, Jun 06 2006

Example

n=4, p[4]=11, 3583=[11011111111] has 11 digits=1 and is prime;
2047=23.89=[11111111111] is not here because it is composite.
a(5)=3583=A081092(266)=A000040(502) having eleven 1's: '110111111111' and A000120(p)<11=prime(5) for primes p<3583.
Mersenne-primes are here, Mersenne composites not.

Mathematica

Do[k=1; While[Count[IntegerDigits[Prime[k], 2], 1] !=Prime[n], k++ ]; Print[Prime[k]], {n, 1, 10}]

Crossrefs

Cf. A000043, A000668, A001348, A061712, A000120, A014499.

Cf. A000040, A000120, A081092.

Sequence in context: A001348 A006515 A093535 * A152058 A057612 A136005

Adjacent sequences: A081090 A081091 A081092 * A081094 A081095 A081096

Keyword

base,nonn

Author

Reinhard Zumkeller, Mar 05 2003

Extensions

More terms from Franklin T. Adams-Watters, Jun 06 2006

Further terms from David Wasserman, Oct 25 2006

Edited by N. J. A. Sloane, Sep 15 2008 at the suggestion of R. J. Mathar

More terms from Sean A. Irvine, Oct 11 2025

Status

approved