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A265753 a(n) = A007949(A265399(n)). 8
0, 0, 1, 0, 1, 1, 2, 0, 2, 1, 3, 1, 5, 2, 2, 0, 8, 2, 13, 1, 3, 3, 21, 1, 2, 5, 3, 2, 34, 2, 55, 0, 4, 8, 3, 2, 89, 13, 6, 1, 144, 3, 233, 3, 3, 21, 377, 1, 4, 2, 9, 5, 610, 3, 4, 2, 14, 34, 987, 2, 1597, 55, 4, 0, 6, 4, 2584, 8, 22, 3, 4181, 2, 6765, 89, 3, 13, 5, 6, 10946, 1, 4, 144, 17711, 3, 9, 233, 35, 3, 28657, 3, 7, 21 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

a(n) = Coefficient of x in the reduction under x^2->x+1 of the polynomial encoded in the prime factorization of n. (Assuming here only polynomials with nonnegative integer coefficients, see e.g. A206296 for the details).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100

FORMULA

a(n) = A007949(A265399(n)).

Other identities. For all n >= 1:

a(A000040(n+1)) = A000045(n). [Maps primes to Fibonacci numbers.]

a(A206296(n)) = A112576(n).

a(A265750(n)) = A192751(n).

PROG

(PARI)

\\ Needs also code from A265398 and A265399.

A265753 = n -> valuation(A265399(n), 3);

for(n=1, 100, write("b265753.txt", n, " ", A265753(n)));

(Scheme) (define (A265753 n) (A007949 (A265399 n)))

CROSSREFS

Cf. A007949, A112576, A192751, A206296, A265399, A265750, A265752.

Cf. also A000040, A000045.

Sequence in context: A304034 A029183 A213423 * A138110 A080233 A156644

Adjacent sequences:  A265750 A265751 A265752 * A265754 A265755 A265756

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 15 2015

STATUS

approved

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Last modified July 17 20:45 EDT 2019. Contains 325109 sequences. (Running on oeis4.)