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 A045584 Numbers k that divide 4^k + 3^k. 2
 1, 7, 49, 343, 2401, 2653, 16807, 18571, 117649, 129997, 823543, 909979, 1005487, 4941601, 5764801, 6369853, 7038409, 34591207, 40353607, 44588971, 49268863, 236474833, 242138449, 282475249, 312122797, 344882041, 381079573, 1655323831, 1694969143, 1872866779, 1977326743 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS MATHEMATICA Select[Range[10^6], Divisible[PowerMod[3, #, #] + PowerMod[4, #, #], #] &] (* Amiram Eldar, Oct 23 2021 *) PROG (Python) from itertools import islice, count def A045584_gen(startvalue=1): # generator of terms >= startvalue kstart = max(startvalue, 1) k3, k4 = 3**kstart, 4**kstart for k in count(kstart): if (k3+k4) % k == 0: yield k k3 *= 3 k4 *= 4 A045584_list = list(islice(A045584_gen(), 10)) # Chai Wah Wu, May 16 2022 (PARI) isok(k) = Mod(4, k)^k + Mod(3, k)^k == 0; \\ Michel Marcus, May 16 2022 CROSSREFS Cf. A074605. Sequence in context: A269774 A269654 A250359 * A228439 A216130 A124536 Adjacent sequences: A045581 A045582 A045583 * A045585 A045586 A045587 KEYWORD nonn AUTHOR EXTENSIONS a(28)-a(31) from Amiram Eldar, Oct 23 2021 STATUS approved

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Last modified February 8 01:34 EST 2023. Contains 360133 sequences. (Running on oeis4.)