A305811 Filter sequence for a(Fibonacci prime) = constant sequences.

1, 2, 2, 3, 2, 4, 5, 6, 7, 8, 9, 10, 2, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 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, 82, 83, 84, 85, 2, 86, 87, 88, 89, 90

Offset

1,2

Comments

Restricted growth sequence transform of the ordered pair [A305800(n), A305820(n)].

For all i, j: a(i) = a(j) => A304105(i) = A304105(j).

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Formula

a(1) = 1; for n > 1, if A010051(n)==1 and A010056(n)==1 [when n is a Fibonacci prime, A005478], a(n) = 2, otherwise a(n) = running count from 3 onward.

Prog

(PARI)
up_to = 100000;
A010056(n) = { my(k=n^2); k+=(k+1)<<2; (issquare(k) || (n>0 && issquare(k-8))) }; \\ From A010056
partialsums(f, up_to) = { my(v = vector(up_to), s=0); for(i=1, up_to, s += f(i); v[i] = s); (v); }
v_partsums = partialsums(x -> (isprime(x)&&A010056(x)), up_to);
A305811(n) = if(1==n, n, if(isprime(n)&&A010056(n), 2, 1+n-v_partsums[n]));

Crossrefs

Cf. A005478, A010051, A010056, A304105, A305800, A305820.

Sequence in context: A305985 A319706 A305894 * A239471 A241509 A268327

Adjacent sequences: A305808 A305809 A305810 * A305812 A305813 A305814

Keyword

nonn

Author

Antti Karttunen, Jun 16 2018

Status

approved