A331977 Integers m such that m and m+1 are terms of A111035.

1, 6479, 11663, 34943, 47519, 51983, 196559, 327359, 685583, 954239, 1016063, 1346879, 2039183, 2332799, 2504447, 4665599, 5143823, 5962319, 6128639, 6723359, 7225343, 9363599, 12027023, 12446783, 14930351, 17639999, 17735759, 22924943, 24681023, 34715519, 41990399

Offset

1,2

Comments

Sequence is infinite as proved by Luca and Marques (2025). - Max Alekseyev, Aug 22 2025

Links

Daniel Suteu, Table of n, a(n) for n = 1..128

Florian Luca and Diego Marques, On integral consecutive arithmetic means of the first Fibonacci numbers. Arch. Math. (2025).

Daniel Yaqubi and Amirali Fatehizadeh, Some results on average of Fibonacci and Lucas sequences, arXiv:2001.11839 [math.CO], 2020.

Prog

(PARI) f(n, m) = (Mod([1, 1; 1, 0], m)^n)[1, 2];
isok(n) = f(n+2, n)==1 && f(n+3, n+1)==1;
for(k=1, 10^7, if(isok(k), print1(k, ", "))); \\ Daniel Suteu, Feb 03 2020

Crossrefs

Cf. A111035 (the sum of the first k nonzero Fibonacci numbers is divisible by k).

Sequence in context: A318629 A213117 A232410 * A339598 A175756 A190012

Adjacent sequences: A331974 A331975 A331976 * A331978 A331979 A331980

Keyword

nonn

Author

Michel Marcus, Feb 03 2020

Extensions

a(23)-a(31) from Daniel Suteu, Feb 03 2020

Status

approved