login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A037896 Primes of the form k^4 + 1. 28
2, 17, 257, 1297, 65537, 160001, 331777, 614657, 1336337, 4477457, 5308417, 8503057, 9834497, 29986577, 40960001, 45212177, 59969537, 65610001, 126247697, 193877777, 303595777, 384160001, 406586897, 562448657, 655360001 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From Bernard Schott, Apr 22 2019: (Start)

These primes are the primitive terms which generate the sequence of integers with only one prime factor and whose Euler's totient is a perfect biquadrate: A307690, so this sequence is a subsequence of A078164 and A307690.

If p prime = k^4 + 1, phi(p) = k^4.

The three last Fermat primes in A019434 {17, 257, 65537} belong to this sequence; with F_k = 2^(2^k) + 1 and for k = 2, 3, 4, phi(F_k) = (2^(2^(k-2)))^4. (End)

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

M. Lal, Primes of the form n^4 + 1, Math. Comp. 21 (1967), pp. 245-247.

EXAMPLE

6^4 + 1 = 1297 is prime.

MATHEMATICA

Select[Range[200]^4+1, PrimeQ] (* Harvey P. Dale, Jul 20 2015 *)

PROG

(PARI) j=[]; for(n=1, 200, if(isprime(n^4+1), j=concat(j, n^4+1))); j

(MAGMA) [n^4+1: n in [1..200] | IsPrime(n^4+1)]; // G. C. Greubel, Apr 28 2019

(Sage) [n^4+1 for n in (1..200) if is_prime(n^4+1)] # G. C. Greubel, Apr 28 2019

CROSSREFS

Cf. A000068, A002523, A019434.

Subsequence of A002496, A078164 and A039770.

Sequence in context: A002590 A029735 A291206 * A099714 A301584 A195443

Adjacent sequences:  A037893 A037894 A037895 * A037897 A037898 A037899

KEYWORD

easy,nonn

AUTHOR

Donald S. McDonald, Feb 27 2000

EXTENSIONS

Corrected and extended by Jason Earls, Jul 19 2001

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 August 24 03:51 EDT 2019. Contains 326260 sequences. (Running on oeis4.)