cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A368811 a(n) = period length of the sequence A020639(n^k - 1), k >= 1.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 1, 1, 12, 1, 10, 1, 1, 1, 60, 1, 10, 1, 1, 1, 18, 1, 2, 1, 1, 1, 660, 1, 66, 1, 1, 1, 1, 1, 10, 1, 1, 1, 4620, 1, 6, 1, 1, 1, 660, 1, 2, 1, 1, 1, 31878, 1, 2, 1, 1, 1, 197340, 1, 5742, 1, 1, 1, 1, 1, 52026, 1, 1, 1, 440220, 1, 28014, 1, 1, 1, 4, 1, 2610, 1, 1, 1, 28014, 1, 2, 1, 1, 1, 3693690, 1, 2, 1, 1, 1, 1, 1, 7590, 1, 1, 1, 1642460820
Offset: 3

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Author

Max Alekseyev, Jan 06 2024

Keywords

Comments

For n = 2, the sequence A020639(n^k - 1) is not periodic (see A049479), but it is such for any n >= 3.
a(n) divides A058254(A000720(A020639(n-1))).

Examples

			a(8) = 2 is the period length of A010705.
a(12) = 12 is the period length of A366717.
		

Crossrefs

Programs

  • PARI
    { a368811(n) = my(r=[], z); forprime(p=2, factor(n-1)[1, 1], if(n%p==0, next); z=znorder(Mod(n, p)); if(!#r || vecmin(apply(x->z%x,r)), r=concat(r,[z])) ); lcm(r); }

Formula

For odd n >= 3, a(n) = 1.

A378559 a(n) = t is the smallest prime t > p = prime(n) for which t == p (mod k) for all k = 2,...,p-1.

Original entry on oeis.org

3, 5, 17, 67, 2531, 27733, 2162177, 12252259, 465585143, 240940299629, 6987268688431, 577614211574437, 48086383113568841, 438120379479182443, 75356705270419372847, 27891400538213970357653, 5584478196651286064932859, 38762848659108926803651261, 23645337682056445350227232067
Offset: 1

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Author

Tamas Sandor Nagy, Nov 30 2024

Keywords

Examples

			a(4) = 67 because prime(4) = 7, and 7 and 67 mod each k = {2, 3, 4, 5, 6} both have remainders {1, 1, 3, 2, 1} in that order, and 67 is the smallest prime after 7 that has this property.
		

Crossrefs

Programs

  • Mathematica
    a[n_] := Module[{p = Prime[n], d}, d = LCM @@ Range[p - 1]; p += d; While[!PrimeQ[p], p += d]; p]; Array[a, 20] (* Amiram Eldar, Dec 01 2024 *)
  • PARI
    a(n) = my(p=prime(n), vr = vector(p-2, k, p % (k+1)), q = nextprime(p+1)); while (vector(p-2, k, q % (k+1)) != vr, q = nextprime(q+1)); q; \\ Michel Marcus, Dec 01 2024

Formula

a(n) == prime(n) (mod A058254(n)). - Amiram Eldar, Dec 01 2024
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