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

0,3

Comments

For all i, j:

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

Links

Table of n, a(n) for n=0..94.

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.

Prog

(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)));

Crossrefs

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

Sequence in context: A144428 A029638 A342297 * A364934 A272831 A290076

Adjacent sequences: A305817 A305818 A305819 * A305821 A305822 A305823

Keyword

nonn

Author

Antti Karttunen, Jun 16 2018

Status

approved