A260641 Numbers k such that 2^k-1 is in A004782 but not in A081767.

2, 3, 7, 9, 12, 13, 17, 23, 25, 26, 31, 33, 37, 41, 44, 45, 46, 48, 49, 55, 56, 57, 61, 65, 67, 71, 72, 73, 80, 81, 82, 85, 87, 89, 91, 93, 95, 97, 100, 101, 106, 107, 109, 111, 113, 114, 117, 121, 126, 127, 129, 133, 135, 136, 139, 141, 142, 143, 145, 147, 151, 159, 160, 161, 163, 164, 165, 173, 174, 175, 176, 177

Offset

1,1

Comments

It appears that the numbers in A004782 \ A081767 are all of the form 2^k-1; this sequence gives the corresponding k-values.

Links

Max Alekseyev, Table of n, a(n) for n = 1..503

M. Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems, sect. 1.3: Binomial coefficients modulo integers, binomod.gp

Prog

(PARI) for(k=2, 999, n=2^k-1; binodiv(2*n-2, n-1, n^2-n) && !binodiv(2*n, n, n^2-1) && print1(k", ")); \\ updated by Max Alekseyev, Jan 22 2026
(Python)
from itertools import count, islice
from oeis_sequences.OEISsequences import binom_mod
def A260641_gen(startvalue=2): # generator of terms >= startvalue
    for k in count(max(startvalue, 2)):
        m = (1<<k)-1
        if not binom_mod(m-1<<1, m-1, m*(m-1)) and binom_mod(m<<1, m, m**2-1):
            yield k
A260641_list = list(islice(A260641_gen(), 10)) # Chai Wah Wu, Jan 11 2026

Crossrefs

Sequence in context: A103797 A262814 A328982 * A077510 A364052 A390986

Adjacent sequences: A260638 A260639 A260640 * A260642 A260643 A260644

Keyword

nonn

Author

M. F. Hasler, Nov 11 2015

Extensions

Terms a(26) onward from Max Alekseyev, Jan 22 2026

Status

approved