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A258328 L.g.f.: log(1 + Sum_{n>=1} x^(n^2) + x^(3*n^2) ). 2
1, -1, 4, -1, 1, -4, 1, -1, 13, -11, 12, -16, 14, -15, 19, -1, 1, -13, 1, -11, 25, -12, 24, -40, 26, -14, 40, -15, 1, -29, 1, -1, 48, -35, 36, -61, 38, -39, 56, -11, 1, -39, 1, -12, 73, -24, 48, -88, 50, -36, 55, -14, 1, -40, 12, -15, 61, -59, 60, -101, 62, -63, 97, -1, 14, -48, 1, -35, 96, -60, 72, -157, 74, -38, 119, -39, 12, -56, 1, -11, 121, -83, 84, -135, 86, -87, 91, -12, 1, -83, 14, -24, 97, -48, 96, -184, 98, -64, 156, -36, 1, -89, 1, -14, 180, -107, 108, -196, 110, -132, 152, -15, 1, -99, 24, -59, 182, -60, 120, -245, 133 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Paul D. Hanna, Table of n, a(n) for n = 1..1024

FORMULA

a(n) = -1 iff n = 2^k for k>=1 [conjecture].

a(p) = +1 for primes p such that 3 is not a square mod p (A003630), and a(n) = +1 nowhere else except at n=0 [conjecture].

EXAMPLE

L.g.f.: L(x) = x - x^2/2 + 4*x^3/3 - x^4/4 + x^5/5 - 4*x^6/6 + x^7/7 - x^8/8 + 13*x^9/9 - 11*x^10/10 + 12*x^11/11 - 16*x^12/12 + 14*x^13/13 - 15*x^14/14 + 19*x^15/15 - x^16/16 +...+ a(n)*x^n/n +...

where

exp(L(x)) = 1 + x + x^3 + x^4 + x^9 + x^12 + x^16 + x^25 + x^27 + x^36 + x^48 + x^49 + x^64 + x^75 + x^81 + x^100 + x^108 +...+ x^(n^2) + x^(3*n^2) +...

Note that for n>1, a(n) = +1 at positions:

[5, 7, 17, 19, 29, 31, 41, 43, 53, 67, 79, 89, 101, 103, 113, 127, ...];

which appears to be A003630 (primes p such that 3 is not a square mod p).

PROG

(PARI) {a(n) = local(L=x); L = log(1 + sum(k=1, sqrtint(n+1), x^(k^2) + x^(3*k^2)) +x*O(x^n)); n*polcoeff(L, n)}

for(n=1, 121, print1(a(n), ", "))

CROSSREFS

Cf. A256357, A003630, A038875.

Sequence in context: A177023 A214333 A080278 * A070085 A131776 A010322

Adjacent sequences:  A258325 A258326 A258327 * A258329 A258330 A258331

KEYWORD

sign

AUTHOR

Paul D. Hanna, Jun 03 2015

STATUS

approved

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Last modified February 28 14:02 EST 2021. Contains 341707 sequences. (Running on oeis4.)