A181743 The exponent k which defines A181741(n) = 2^t-2^k-1.

2, 1, 3, 2, 1, 3, 1, 5, 4, 2, 1, 7, 6, 5, 4, 2, 7, 5, 3, 1, 5, 2, 1, 3, 9, 7, 4, 2, 1, 11, 13, 10, 8, 6, 1, 11, 7, 4, 11, 3, 17, 14, 13, 9, 8, 6, 5, 4, 2, 11, 19, 18, 17, 14, 12, 11, 10, 9, 7, 4, 2, 1, 17, 9, 7, 3, 16, 10, 5, 4, 1, 21, 15, 13, 10, 5, 4, 1, 13, 9, 2

Offset

1,1

Links

Table of n, a(n) for n=1..81.

Formula

k = A007814(A181741(n)+1). [R. J. Mathar, Nov 18 2010]

Mathematica

IntegerExponent[Select[Table[2^t-2^k-1, {t, 1, 20}, {k, 1, t-1}] // Flatten // Union, PrimeQ] + 1, 2] (* Amiram Eldar, Dec 17 2018 after Jean-François Alcover at A181741 *)

Prog

(PARI) listk(nn) = {for (n=3, nn, forstep(k=n-1, 1, -1, if (isprime(2^n-2^k-1), print1(k, ", ")); ); ); } \\ Michel Marcus, Dec 17 2018
(Python)
from itertools import count, islice
from sympy import isprime
def A181743_gen(): # generator of terms
    m = 2
    for t in count(1):
        r=1<<t-1
        for k in range(t-1, 0, -1):
            if isprime(m-r-1):
                yield k
            r>>=1
        m<<=1
A181743_list=list(islice(A181743_gen(), 30)) # Chai Wah Wu, Jul 08 2022

Crossrefs

Cf. A181741, A181742.

Sequence in context: A240554 A107338 A118123 * A330727 A174737 A131756

Adjacent sequences: A181740 A181741 A181742 * A181744 A181745 A181746

Keyword

nonn

Author

Vladimir Shevelev, Nov 08 2010

Extensions

Terms equivalent to insertions in A181741 inserted by R. J. Mathar, Nov 18 2010

More terms from Michel Marcus, Dec 17 2018

Status

approved