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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A343116 a(n) is the Pisano period of prime(n)^2.

Original entry on oeis.org

6, 24, 100, 112, 110, 364, 612, 342, 1104, 406, 930, 2812, 1640, 3784, 1504, 5724, 3422, 3660, 9112, 4970, 10804, 6162, 13944, 3916, 19012, 5050, 21424, 7704, 11772, 8588, 32512, 17030, 37812, 6394, 22052, 7550, 49612, 53464, 56112, 60204, 31862, 16290, 36290
Offset: 1

Views

Author

Felix Fröhlich, Apr 05 2021

Keywords

Crossrefs

Cf. A001175, A001248, A060305.

Programs

  • PARI
    \\ After Charles R Greathouse IV in A001175 (Start)
fibmod(n, m)=((Mod([1, 1; 1, 0], m))^n)[1, 2]
entryp(p)=my(k=p+[0, -1, 1, 1, -1][p%5+1], f=factor(k)); for(i=1, #f[, 1], for(j=1, f[i, 2], if((Mod([1, 1; 1, 0], p)^(k/f[i, 1]))[1, 2], break); k/=f[i, 1])); k
entry(n)=if(n==1, return(1)); my(f=factor(n), v); v=vector(#f~, i, if(f[i, 1]>1e14, entryp(f[i, 1]^f[i, 2]), entryp(f[i, 1])*f[i, 1]^(f[i, 2] - 1))); if(f[1, 1]==2&&f[1, 2]>1, v[1]=3<

Formula

a(n) = A001175(A001248(n)).

A106292 Period of the Lucas sequence A000032 mod prime(n).

Original entry on oeis.org

3, 8, 4, 16, 10, 28, 36, 18, 48, 14, 30, 76, 40, 88, 32, 108, 58, 60, 136, 70, 148, 78, 168, 44, 196, 50, 208, 72, 108, 76, 256, 130, 276, 46, 148, 50, 316, 328, 336, 348, 178, 90, 190, 388, 396, 22, 42, 448, 456, 114, 52, 238, 240, 250, 516, 176, 268, 270, 556, 56
Offset: 1

Views

Author

T. D. Noe, May 02 2005

Keywords

Comments

This sequence differs from A060305 at only one position: 3, which corresponds to the prime 5, which is the discriminant of the characteristic polynomial x^2-x-1. We have a(n) < prime(n) for the primes in A038872.

Links

Crossrefs

Cf. A060305 (period of Fibonacci numbers mod prime(n)), A106273 (discriminant of the polynomial x^n-x^(n-1)-...-x-1), A106291.

Programs

  • Mathematica
    n=2; Table[p=Prime[i]; a=Join[Table[ -1, {n-1}], {n}]; a=Mod[a, p]; a0=a; k=0; While[k++; s=Mod[Plus@@a, p]; a=RotateLeft[a]; a[[n]]=s; a!=a0]; k, {i, 70}]

Formula

a(n) = A106291(prime(n)).

A343117 a(n) is the absolute difference between the Pisano periods of prime(n)^2 and prime(n).

Original entry on oeis.org

3, 16, 80, 96, 100, 336, 576, 324, 1056, 392, 900, 2736, 1600, 3696, 1472, 5616, 3364, 3600, 8976, 4900, 10656, 6084, 13776, 3872, 18816, 5000, 21216, 7632, 11664, 8512, 32256, 16900, 37536, 6348, 21904, 7500, 49296, 53136, 55776, 59856, 31684, 16200, 36100
Offset: 1

Views

Author

Felix Fröhlich, Apr 05 2021

Keywords

Comments

a(n) = 0 if and only if prime(n) is a Wall-Sun-Sun (Fibonacci-Wieferich) prime.

Links

Crossrefs

Cf. A000040, A001175, A001248, A060305, A343116.

Programs

  • PARI
    \\ After Charles R Greathouse IV in A001175 (Start)
fibmod(n, m)=((Mod([1, 1; 1, 0], m))^n)[1, 2]
entryp(p)=my(k=p+[0, -1, 1, 1, -1][p%5+1], f=factor(k)); for(i=1, #f[, 1], for(j=1, f[i, 2], if((Mod([1, 1; 1, 0], p)^(k/f[i, 1]))[1, 2], break); k/=f[i, 1])); k
entry(n)=if(n==1, return(1)); my(f=factor(n), v); v=vector(#f~, i, if(f[i, 1]>1e14, entryp(f[i, 1]^f[i, 2]), entryp(f[i, 1])*f[i, 1]^(f[i, 2] - 1))); if(f[1, 1]==2&&f[1, 2]>1, v[1]=3<

Formula

a(n) = abs(A343116(n)-A060305(n)) = abs(A001175(A001248(n))-A001175(A000040(n))).
Previous Showing 11-13 of 13 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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