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A022521 (n+1)^5 - n^5. 20
1, 31, 211, 781, 2101, 4651, 9031, 15961, 26281, 40951, 61051, 87781, 122461, 166531, 221551, 289201, 371281, 469711, 586531, 723901, 884101, 1069531, 1282711, 1526281, 1803001, 2115751, 2467531 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Last digit of a(n) is always 1. Last two digits of a(n) Mod[a(n),100] are repeated periodically with palindromic period of length 20 {1,31,11,81,1,51,31,61,81,51,51,81,61,31,51,1,81,11,31,1}. Last three digits of a(n) Mod[a(n),1000] are repeated periodically with palindromic period of length 200. - Alexander Adamchuk, Aug 11 2006

In Conway and Guy, these numbers are called nexus numbers of order 5. - M. F. Hasler, Jan 27 2013

REFERENCES

J. H. Conway and R. K. Guy, The Book of Numbers, p. 54.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

Sequence is 24*0+1, 24*1+7, 24*8+19, 24*31+37, ... = A003215 + 24 * A006322. - Xavier Acloque Oct 11 2003

G.f.: (-1-x^4-26*x^3-66*x^2-26*x)/(x-1)^5. [Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]

MATHEMATICA

q=5; lst={}; Do[AppendTo[lst, (n+1)^q-n^q], {n, 0, 5!}]; lst - Vladimir Joseph Stephan Orlovsky, Jan 23 2009

Table[(n+1)^5-n^5, {n, 0, 30} (* Vincenzo Librandi, Nov 23 2011 *)

PROG

(MAGMA) [(n+1)^5-n^5: n in [0..30]]; // Vincenzo Librandi, Nov 23 2011

(PARI) a(n)=(n+1)^5-n^5 \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

First differences of A000584. A row of A047969.

Sequence in context: A096906 A181124 A142328 * A152730 A090027 A164784

Adjacent sequences:  A022518 A022519 A022520 * A022522 A022523 A022524

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 30 20:18 EDT 2017. Contains 284302 sequences.