login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A095366 Least k > 1 such that k divides 1^n + 2^n +...+ (k-1)^n. 4
3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 17, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5, 3, 7, 3, 5, 3, 7, 3, 5, 3, 11, 3, 5, 3, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is similar to A094756 but seems to have a simpler periodicity rules:

a(n)=3 when n=1 (mod 2), otherwise

a(n)=5 when n=2 (mod 4), otherwise

a(n)=7 when n=4*m (mod 12) for some m=1,2, otherwise

a(n)=11 when n=12*m (mod 60) for some m=1,2,3,4, otherwise

a(n)=17 when n=60*m (mod 240) for some m=1,2,3, otherwise

a(n)=19 when n=240*m (mod 720) for some m=1,2, otherwise

a(n)=23 when n=720*m (mod 7920) for some m=1,..,10, etc.

Note that only odd primes p given by A095365 seem to appear in this sequence. Given the definition of f(p) in that sequence, let q=A095365(i) and p=A095365(i-1), then the general rule for this sequence seems to be a(n)=q when n=f(p)*m (mod f(q)) for some m=1,...,f(q)/f(p)-1

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

EXAMPLE

a(4) = 7 because k divides 1^4 + 2^4 +...+ k^4 for k=7 but no smaller k > 1.

MATHEMATICA

Table[k=2; s=0; While[s=s+(k-1)^n; Mod[s, k]>0, k++ ]; k, {n, 100}]

PROG

(PARI) A095366(n) = { my(k=1, s=0); while(1, k++; s += ((k-1)^n); if(!(s%k), return(k))); }; \\ Antti Karttunen, Dec 19 2018

CROSSREFS

Cf. A094756, A095365.

Sequence in context: A118271 A260689 A328386 * A029604 A079602 A075572

Adjacent sequences:  A095363 A095364 A095365 * A095367 A095368 A095369

KEYWORD

nonn

AUTHOR

T. D. Noe, Jun 03 2004

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 24 07:17 EDT 2021. Contains 347623 sequences. (Running on oeis4.)