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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

Table of n, a(n) for n=1..11.

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

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