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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A268511 Odd integers n such that 3^n + 5^n = x^2 + y^2 (x and y integers) is solvable. 0
 1, 5, 13, 17, 29, 89, 109, 149, 157, 193, 373 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Corresponding 3^n + 5^n values are 8, 3368, 1222297448, 763068593288, 186264583553473068008, ... 445 <= a(12) <= 509. 509, 661, 709 are terms. - Chai Wah Wu, Jul 22 2020 LINKS EXAMPLE 1 is a term because 3^1 + 5^1 = 8 = 2^2 + 2^2. 5 is term because 3^5 + 5^5 = 3368 = 2^2 + 58^2. 13 is a term because 3^13 + 5^13 = 1222297448 = 4118^2 + 34718^2. MATHEMATICA Select[Range[1, 110, 2], Resolve@ Exists[{x, y}, Reduce[3^# + 5^# == (x^2 + y^2), {x, y}, Integers]] &] (* Michael De Vlieger, Feb 07 2016 *) PROG (PARI) is(n) = #bnfisintnorm(bnfinit(z^2+1), n); for(n=1, 1e3, if(n%2==1 && is(3^n + 5^n), print1(n, ", "))); (Python) from sympy import factorint A268511_list = [] for n in range(1, 50, 2):     m = factorint(3**n+5**n)     for d in m:         if d % 4 == 3 and m[d] % 2:             break     else:         A268511_list.append(n) # Chai Wah Wu, Dec 26 2018 CROSSREFS Cf. A001481, A074606. Sequence in context: A145016 A123079 A273950 * A038938 A253079 A184851 Adjacent sequences:  A268508 A268509 A268510 * A268512 A268513 A268514 KEYWORD nonn,more AUTHOR Altug Alkan, Feb 06 2016 EXTENSIONS a(8)-a(9) from Giovanni Resta, Apr 10 2016 a(10)-a(11) 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.

Last modified September 21 14:54 EDT 2020. Contains 337272 sequences. (Running on oeis4.)