A305820 Filter sequence for a(Fibonacci numbers > 1) = constant sequences.

0, 1, 2, 2, 3, 2, 4, 5, 2, 6, 7, 8, 9, 2, 10, 11, 12, 13, 14, 15, 16, 2, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 2, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 2, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 2, 82, 83, 84, 85, 86

Offset: 0

Author

Antti Karttunen, Jun 16 2018

Keywords

• nonn

Comments

For all i, j:

a(i) = a(j) => A003603(i) = A003603(j) => A304101(i) = A304101(j) => A007895(i) = A007895(j).

Crossrefs

Cf. A000045, A003603, A007895, A010056, A072649, A304101.

Programs

PARI

A010056(n) = { my(k=n^2); k+=(k+1)<<2; (issquare(k) || (n>0 && issquare(k-8))) }; \\ From A010056
A072649(n) = { my(m); if(n<1, 0, m=0; until(fibonacci(m)>n, m++); m-2); }; \\ From A072649
A305820(n) = if(n<=1, n, if(1==A010056(n),2,2+n-A072649(n)));

Formula

a(0)= 0, a(1) = 1, for n > 1, a(n) = 2 if n is a Fibonacci number > 1, otherwise a(n) = 2+n-A072649(n) = running count from 3 onward for non-Fibonacci numbers.