login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons 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 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A269833 Numbers n such that 2^n + n! is the sum of 2 squares. 0
0, 4, 6, 8, 16, 20, 21, 40, 45, 47, 52, 64, 67, 71, 72, 74, 88 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Integers n such that the equation 2^n + n! = x^2 + y^2 where x and y are integers is solvable.

4, 8, 16 and 64 are powers of 2. What is the next power of 2 (if any) in this sequence?

103 <= a(18) <= 108. 108, 117, 144, 176, 254, 537 are terms. - Chai Wah Wu, Jul 22 2020

LINKS

Table of n, a(n) for n=1..17.

EXAMPLE

6 is a term because 2^6 + 6! = 28^2.

8 is a term because 2^8 + 8! = 24^2 + 200^2.

21 is a term because 2^21 + 21! = 1222129664^2 + 7042537984^2.

MATHEMATICA

Select[Range[0, 64], SquaresR[2, 2^# + #!] > 0 &] (* Michael De Vlieger, Mar 07 2016 *)

PROG

PARI) isA001481(n) = #bnfisintnorm(bnfinit(z^2+1), n);

for(n=0, 1e2, if(isA001481(n!+2^n), print1(n, ", ")));

CROSSREFS

Cf. A001481, A007611.

Sequence in context: A055397 A239412 A295006 * A049421 A260314 A238269

Adjacent sequences:  A269830 A269831 A269832 * A269834 A269835 A269836

KEYWORD

nonn,more

AUTHOR

Altug Alkan, Mar 06 2016

EXTENSIONS

a(17) from Chai Wah Wu, Jul 22 2020

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 December 1 22:12 EST 2021. Contains 349435 sequences. (Running on oeis4.)