login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A279095 Smallest k such that sigma(2^(k*n)) is prime. 0
1, 1, 2, 1, 6, 1, 18, 2, 2, 3, 8, 1, 40, 9, 2, 1, 177728, 1, 120, 3, 6, 4, 32906, 95, 868, 20, 1648, 346 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Equivalently, smallest k such that k*n + 1 is a Mersenne exponent (A000043).

As of Mar 11 2017, the j-th Mersenne exponent A000043(j) is known for j=1..45; four additional terms of A000043 are listed in the Extensions for that sequence, but it is not yet known whether they are A000043(46) through A000043(49). None of the first 45 Mersenne exponents are of the form k*29 + 1, so a(29) > floor((A000043(45) - 1)/29) = floor((37156667 - 1)/29) = 1281264. However, one of the four additional terms is 57885161 = 1996040*29 + 1; thus, 1281264 < a(29) <= 1996040.

a(30) through a(38) are 1, 700, 623, 134, 88864, 284, 1236, 821688, 60.

a(39) > floor((A000043(45) - 1)/39) = 952735.

This sequence coincides with A186283 (Least number k such that k*n+1 is a prime dividing 2^n-1) from a(2) through a(8), but a(9) = 2 whereas A186283(9) = 8.

LINKS

Table of n, a(n) for n=1..28.

EXAMPLE

a(1) = 1 because sigma(2^(1*1)) = sigma(2) = 1 + 2 = 3 is prime. (1*1 + 1 = 2 = A000043(1).)

a(3) = 2 because sigma(2^(1*3)) = sigma(2^3) = 1 + 2 + 4 + 8 = 15 is not prime, but sigma(2^(2*3)) = sigma(2^6) = 1 + 2 + 4 + 8 + 16 + 32 + 64 = 127 is prime. (1*3 + 1 = 4 is not in A000043, but 2*3 + 1 = 7 = A000043(4).)

a(17) = 177728 because sigma(2^(177728*17)) is prime and sigma(2^(k*17)) is not prime for any k < 177728. (177728*17 + 1 = 3021377 = A000043(37), and no Mersenne exponent less than A000043(37) is of the form k*17 + 1.)

PROG

(PARI) a(n) = k=1; while(!isprime(sigma(2^(k*n))), k++); k; \\ Michel Marcus, Mar 12 2017

CROSSREFS

Cf. A000043, A000203, A186283, A279004.

Sequence in context: A322672 A225769 A280736 * A186283 A307374 A173279

Adjacent sequences:  A279092 A279093 A279094 * A279096 A279097 A279098

KEYWORD

nonn,hard,more

AUTHOR

Jon E. Schoenfield, Mar 11 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 20 23:20 EST 2020. Contains 331104 sequences. (Running on oeis4.)