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A232395 (ceiling(sqrt(n^3 + n^2 + n + 1)))^2 - (n^3 + n^2 + n + 1). 3
0, 0, 1, 9, 15, 13, 30, 0, 40, 21, 45, 57, 51, 21, 70, 105, 120, 109, 66, 156, 43, 77, 81, 49, 216, 108, 217, 9, 36, 21, 293, 192, 31, 189, 309, 385, 411, 381, 289, 129, 408, 112, 281, 396, 451, 440, 357, 196, 624, 309, 613, 120, 276, 360, 366, 288, 120, 725 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(n)=0, iff 1 + n + n^2 + n^3 is a perfect square. For example, a(7)=0 and we have 1 + 7 + 7^2 + 7^3 = 20^2.

a(n) = Difference between smallest square >= (n^3 + n^2 + n + 1) and (n^3 + n^2 + n + 1) - Antti Karttunen, Nov 27 2013

LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..1000

FORMULA

Contribution from Antti Karttunen, Nov 27 2013: (Start)

a(n) = A000290(⌈sqrt(A053698(n))⌉) - A053698(n). Where ⌈x⌉ stands for ceiling(x). This further reduces as:

a(n) = A000290(A135034(A053698(n))) - A053698(n).

a(n) = A048761(A053698(n)) - A053698(n).

a(n) = A068527(A053698(n)).

(End)

PROG

(PARI) a(n) = ceil(sqrt(n^3+n^2+n+1))^2 - (n^3+n^2+n+1); \\ Michel Marcus, Nov 23 2013

CROSSREFS

Cf. A053698, A068527.

Sequence in context: A073920 A130119 A346609 * A184048 A284128 A058957

Adjacent sequences: A232392 A232393 A232394 * A232396 A232397 A232398

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Nov 23 2013

EXTENSIONS

More terms from Peter J. C. Moses

STATUS

approved

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Last modified December 2 12:34 EST 2022. Contains 358496 sequences. (Running on oeis4.)