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

Author

Antti Karttunen, Jun 16 2018

Keywords

• nonn

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

Crossrefs

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

Programs

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]));

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.