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

Author

Michel Marcus, Feb 03 2020

Keywords

• nonn

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.

Crossrefs

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

Programs

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

Extensions

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