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A305811 Filter sequence for a(Fibonacci prime) = constant sequences. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 14 17:43 EDT 2019. Contains 328022 sequences. (Running on oeis4.)