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 1-5 of 5 results.

A355597 a(1) = 2. For n > 1, a(n) = smallest prime q such that q^(a(n-1)-1) == 1 (mod a(n-1)^2).

Original entry on oeis.org

2, 5, 7, 19, 127, 911, 7331, 167149, 387749, 17153317, 432383657, 10459192927
Offset: 1

Views

Author

Felix Fröhlich, Jul 09 2022

Keywords

Comments

Is this an increasing sequence or does it enter a cycle?

Crossrefs

Row n = 1 of A249162.
Cf. A355598, A355599, A355600, A355601, A355602.

Programs

  • PARI
    seq(start, terms) = my(x=start, i=1); print1(start, ", "); while(1, forprime(q=1, , if(Mod(q, x^2)^(x-1)==1, print1(q, ", "); x=q; i++; if(i >= terms, break({2}), break))))
seq(2, 20) \\ Print initial 20 terms of sequence

A355598 a(1) = 3. For n > 1, a(n) = smallest prime q such that q^(a(n-1)-1) == 1 (mod a(n-1)^2).

Original entry on oeis.org

3, 17, 131, 659, 503, 9833, 49603, 327317, 13900147, 144229223, 5872276013
Offset: 1

Views

Author

Felix Fröhlich, Jul 09 2022

Keywords

Comments

Is this overall an increasing sequence or does it enter a cycle?
The sequence decreases for the first time at n = 5.

Crossrefs

Row n = 2 of A249162.
Cf. A355597, A355599, A355600, A355601, A355602.

Programs

  • Mathematica
    sp[n_]:=Module[{p=2},While[PowerMod[p,n-1,n^2]!=1,p=NextPrime[p]];p]; NestList[sp,3,8] (* Harvey P. Dale, Jul 23 2023 *)
  • PARI
    seq(start, terms) = my(x=start, i=1); print1(start, ", "); while(1, forprime(q=1, , if(Mod(q, x^2)^(x-1)==1, print1(q, ", "); x=q; i++; if(i >= terms, break({2}), break))))
seq(3, 20) \\ Print initial 20 terms of sequence

A355599 a(1) = 29. For n > 1, a(n) = smallest prime q such that q^(a(n-1)-1) == 1 (mod a(n-1)^2).

Original entry on oeis.org

29, 41, 313, 1499, 941, 12011, 6287, 52301, 50077, 137743, 1274353, 46303409, 89018221, 687655393, 7462816891
Offset: 1

Views

Author

Felix Fröhlich, Jul 09 2022

Keywords

Comments

Is this overall an increasing sequence or does it enter a cycle?
The sequence decreases for the first time at n = 5.

Crossrefs

Row n = 10 of A249162.
Cf. A355597, A355598, A355600, A355601, A355602.

Programs

  • PARI
    seq(start, terms) = my(x=start, i=1); print1(start, ", "); while(1, forprime(q=1, , if(Mod(q, x^2)^(x-1)==1, print1(q, ", "); x=q; i++; if(i >= terms, break({2}), break))))
seq(29, 20) \\ Print initial 20 terms of sequence

A355600 a(1) = 37. For n > 1, a(n) = smallest prime q such that q^(a(n-1)-1) == 1 (mod a(n-1)^2).

Original entry on oeis.org

37, 691, 19181, 5849, 18503, 37853, 478741, 18401827, 571007279, 5860639859
Offset: 1

Views

Author

Felix Fröhlich, Jul 09 2022

Keywords

Comments

Is this overall an increasing sequence or does it enter a cycle?
The sequence decreases for the first time at n = 4.

Crossrefs

Row n = 12 of A249162.
Cf. A355597, A355598, A355599, A355601, A355602.

Programs

  • PARI
    seq(start, terms) = my(x=start, i=1); print1(start, ", "); while(1, forprime(q=1, , if(Mod(q, x^2)^(x-1)==1, print1(q, ", "); x=q; i++; if(i >= terms, break({2}), break))))
seq(37, 20) \\ Print initial 20 terms of sequence

A355601 a(1) = 47. For n > 1, a(n) = smallest prime q such that q^(a(n-1)-1) == 1 (mod a(n-1)^2).

Original entry on oeis.org

47, 53, 521, 6037, 3347, 4931, 105667, 1131259, 4739509, 175166071, 3834885547
Offset: 1

Views

Author

Felix Fröhlich, Jul 09 2022

Keywords

Comments

Is this overall an increasing sequence or does it enter a cycle?
The sequence decreases for the first time at n = 5.

Crossrefs

Row n = 15 of A249162.
Cf. A355597, A355598, A355599, A355600, A355602.

Programs

  • Mathematica
    nxt[a_]:=Module[{q=3},While[PowerMod[q,a-1,a^2]!=1,q=NextPrime[q]];q]; NestList[ nxt,47,10] (* The program will take a long time to run. *) (* Harvey P. Dale, Jan 31 2023 *)
  • PARI
    seq(start, terms) = my(x=start, i=1); print1(start, ", "); while(1, forprime(q=1, , if(Mod(q, x^2)^(x-1)==1, print1(q, ", "); x=q; i++; if(i >= terms, break({2}), break))))
seq(47, 20) \\ Print initial 20 terms of sequence
Showing 1-5 of 5 results.

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