login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A259835 a(n) is the number of odd primes of the form b^(2^n)+1 that are less than A123599(n+1). 1
1, 1, 1, 1, 41, 152, 122, 185, 8, 860, 24, 612, 97094 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A generalized Fermat prime b^(2^n)+1 can be thought of as belonging to the "family" n. Then a(n) counts how many generalized Fermat primes in family n precede the first generalized Fermat prime in family n+1.

Each family as defined here is a subset of its preceding family, in the sense that b^(2^n) + 1 = (b^2)^(2^(n-1)) + 1.

a(12) is expected to be near 97000.

LINKS

Table of n, a(n) for n=0..12.

Y. Gallot, Status of the smallest base values yielding Generalized Fermat primes.

EXAMPLE

To find a(5), find all primes b^32 + 1 until you reach a base b that is a perfect square. In this case you find 152 nonsquare b values { 30, 54, 96, 112, ..., 10396 }, but the 153rd b is 10404, a perfect square. So 10404^32 + 1 = 102^64 + 1 belongs to the next family. Therefore a(5)=152.

PROG

(PARI) b=2; for(n=0, 100, x=0; until(, if(ispseudoprime(b^(2^n)+1), if(issquare(b, &b), break, x++)); b+=2); print("a(", n, ")=", x, ", next b is ", b))

CROSSREFS

Cf. A056993, A123599.

Sequence in context: A141957 A108016 A142630 * A082252 A221811 A105100

Adjacent sequences: A259832 A259833 A259834 * A259836 A259837 A259838

KEYWORD

nonn,more,hard

AUTHOR

Jeppe Stig Nielsen, Jul 06 2015

EXTENSIONS

a(12) via b-file of A088362 from Jeppe Stig Nielsen, Feb 16 2022

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 26 21:15 EST 2022. Contains 358362 sequences. (Running on oeis4.)