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.

Showing 1-6 of 6 results.

A074792 Least k > 1 such that k^n == 1 (mod n).

Original entry on oeis.org

2, 3, 4, 3, 6, 5, 8, 3, 4, 9, 12, 5, 14, 13, 16, 3, 18, 5, 20, 3, 4, 21, 24, 5, 6, 25, 4, 13, 30, 11, 32, 3, 34, 33, 36, 5, 38, 37, 16, 3, 42, 5, 44, 21, 16, 45, 48, 5, 8, 9, 52, 5, 54, 5, 16, 13, 7, 57, 60, 7, 62, 61, 4, 3, 66, 23, 68, 13, 70, 29, 72, 5, 74, 73, 16, 37, 78, 17, 80, 3
Offset: 1

Views

Author

Benoit Cloitre, Sep 07 2002

Keywords

Links

Crossrefs

a(n) = {A076944(n)}^(1/n).
Cf. A076942, A076943, A076944.

Programs

  • Mathematica
    Do[k = 2; While[ !IntegerQ[(k^n - 1)/n], k++ ]; Print[k], {n, 1, 80}] (* Robert G. Wilson v *)
  • PARI
    a(n)=if(n<0,0,s=2; while((s^n-1)%n>0,s++); s)
  • PARI
    a(n)=my(s=2); while(Mod(s,n)^n-1!=0, s++); return(s) \\ Rémy Sigrist, Apr 02 2017

Formula

If p is prime a(p)=p+1 and a(2p)=2p-1; if n is in A050384 a(n)=n+1; if n is in A067945 a(n)=3 etc. It seems that sum(k=1, n, a(k)) is asymptotic to c*n^2 with c=0.2...

A193746 Smallest k such that k*n^2 +1 is an n-th power.

Original entry on oeis.org

1, 2, 7, 5, 311, 434, 42799, 90075, 12345679, 34867844, 6140565047, 1695421, 4696537119847, 20088655029078, 5124095576030431, 25657845139503479, 7563707819165039903, 43404581642184336392, 14523213296398891966759
Offset: 1

Views

Author

Michel Lagneau, Aug 03 2011

Keywords

Examples

			a(9) = 12345679 because 12345679*9^2+1 = 1000000000 = 10^9.

Crossrefs

Cf. A076943.

Programs

  • Mathematica
    a={}; Do[k = 2;While[ !IntegerQ[(k^n - 1)/n^2], k++ ]; AppendTo[a,(k^n-1)/n^2], {n, 1, 20}]; a
  • PARI
    a(n)=my(k);while(!ispower(k++*n^2+1,n),);k \\ Charles R Greathouse IV, May 15 2013

A216439 Smallest k such that k*n^3 + 1 is an n-th power.

Original entry on oeis.org

1, 1, 37, 791, 95051, 111748, 2277696793, 484679258335, 229930796172439, 79792266297612, 66954547910007962117, 337165646545, 45082285083777592171142467, 2379140952844779936142872, 60722942736706550906445847537201, 78033832840595333890814363993704319
Offset: 1

Views

Author

Michel Lagneau, Sep 10 2012

Keywords

Examples

			a(3) = 37 because 37*3^3 + 1 = 1000 = 10^3.

Links

Crossrefs

Cf. A076943, A193746.

Programs

  • Maple
    f:= proc(n) local S,x;
  S:= subs(1=n^3+1, map(t -> rhs(op(t)), [msolve(x^n-1, n^3)]));
  x:= min(S);
  (x^n-1)/n^3
end proc:
f(1):= 1:
map(f, [$1..20]); # Robert Israel, Aug 26 2020
  • Mathematica
    a={}; Do[k = 2; While[ !IntegerQ[(k^n - 1)/n^3], k++ ]; AppendTo[a, (k^n-1)/n^3], {n, 1, 20}]; a

A076944 Least number such that n*k+1 is an n-th power.

Original entry on oeis.org

2, 9, 64, 81, 7776, 15625, 2097152, 6561, 262144, 3486784401, 743008370688, 244140625, 793714773254144, 3937376385699289, 1152921504606846976, 43046721, 2185911559738696531968, 3814697265625
Offset: 1

Views

Author

Amarnath Murthy, Oct 19 2002

Keywords

Comments

a(n) <= {(n+1)^n - 1}/n.

Crossrefs

Cf. A076942, A076943, A074792.

Programs

  • Mathematica
    Do[k = 2; While[ !IntegerQ[(k^n - 1)/n], k++ ]; Print[k^n], {n, 1, 19}]

Formula

a(n) = n*A076943(n) + 1.

Extensions

Edited, corrected and extended by Robert G. Wilson v, Oct 21 2002

A216471 Smallest k such that k*n^4 + 1 is an n-th power.

Original entry on oeis.org

1, 3, 271, 61535, 50812751, 21358519, 237419801716063, 1135029771535910655, 8972959412935210028959, 91620671606331844031, 1599468651197092802422012477487, 702649782312030280795815963215, 978557919186290794806960014681034796687
Offset: 1

Views

Author

Michel Lagneau, Sep 10 2012

Keywords

Examples

			a(3) = 271 because 271*3^4 + 1 = 21952 = 28^3.

Crossrefs

Cf. A076943, A193746, A216439.

Programs

  • Mathematica
    a={}; Do[k = 2; While[ !IntegerQ[(k^n - 1)/n^4], k++ ]; AppendTo[a, (k^n-1)/n^4], {n, 1, 20}]; a

A216472 Smallest k such that k*n^5 + 1 is an n-th power.

Original entry on oeis.org

1, 7, 2269, 4129151, 30762501251, 2239747210, 27448639374405504361, 2413133306001931169183743, 382044091289242990177493431399, 92389875896827641843360078, 41175701028835553188828526348886198418157, 251171485090270512606177135871202294053615
Offset: 1

Views

Author

Michel Lagneau, Sep 10 2012

Keywords

Examples

			a(3) = 2269 because 2269*3^5 + 1 = 551368 =  82^3.

Crossrefs

Cf. A076943, A193746, A216439, A216471.

Programs

  • Mathematica
    a={}; Do[k = 2; While[ !IntegerQ[(k^n - 1)/n^5], k++ ]; AppendTo[a, (k^n-1)/n^5], {n, 1, 20}]; a
Showing 1-6 of 6 results.

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