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 1-7 of 7 results.

A111739 Distance between k*(n-th prime) and next prime, k=7 case.

Original entry on oeis.org

3, 2, 2, 4, 2, 6, 8, 4, 2, 8, 6, 4, 6, 6, 2, 2, 6, 4, 10, 2, 10, 4, 6, 8, 4, 2, 6, 2, 6, 6, 18, 2, 8, 4, 6, 4, 4, 10, 2, 2, 6, 10, 24, 10, 2, 6, 4, 6, 8, 4, 6, 20, 6, 2, 2, 6, 6, 4, 10, 6, 6, 2, 4, 2, 12, 2, 16, 12, 8, 4, 2, 8, 10, 6, 4, 2, 6, 10, 12, 16, 6, 6, 2, 6, 6, 8, 20, 4, 2, 10, 2, 6, 4, 12, 6, 6, 8
Offset: 1

Views

Author

Zak Seidov, Nov 18 2005

Keywords

Comments

Other cases: k=1 A001223 Differences between consecutive primes, k=2 A059787, k=3 A114245, k=4 A114246, k=5 A114247, k=6 A114248, k=8 A111740, k=9 A111741, k=10 A111742.

Examples

			a(1)=3 because prime(1)=2 and 7*2+1=17 (prime).

Links

Crossrefs

Cf. A001223, A059787, A114245, A114246, A114247, A114248, A111740, A111741, A111742.

Programs

  • Mathematica
    dnp[n_]:=Module[{c=7*Prime[n]},NextPrime[c]-c]; Array[dnp,100] (* Harvey P. Dale, Jan 14 2022 *)

A111740 Distance between k*(n-th prime) and next prime, k=8 case.

Original entry on oeis.org

1, 5, 1, 3, 1, 3, 1, 5, 7, 1, 3, 11, 3, 3, 3, 7, 7, 3, 5, 1, 3, 9, 9, 7, 11, 1, 3, 1, 5, 3, 3, 1, 1, 5, 1, 5, 3, 3, 25, 15, 1, 3, 3, 5, 3, 5, 5, 3, 7, 15, 3, 1, 3, 3, 7, 7, 1, 11, 5, 3, 3, 3, 3, 15, 17, 3, 9, 3, 1, 5, 9, 7, 3, 15, 5, 3, 7, 5, 1, 27, 7, 3, 1, 3, 5, 3, 1, 3, 3, 5, 3, 1, 11, 1, 9, 3, 1, 9, 17
Offset: 1

Views

Author

Zak Seidov, Nov 18 2005

Keywords

Comments

Other cases: k=1 A001223 Differences between consecutive primes, k=2 A059787, k=3 A114245, k=4 A114246, k=5 A114247, k=6 A114248, k=7 A111739, k=9 A111741, k=10 A111742.

Examples

			a(1)=1 because prime(1)=2 and 8*2+1=17 (prime).

Crossrefs

Cf. A001223, A059787, A114245, A114246, A114247, A114248, A111739, A111741, A111742.

A111741 Distance between k*(n-th prime) and next prime, k=9 case.

Original entry on oeis.org

1, 2, 2, 4, 2, 10, 4, 2, 4, 2, 2, 4, 4, 2, 8, 2, 10, 8, 4, 2, 2, 8, 4, 8, 4, 2, 2, 4, 2, 2, 8, 2, 4, 8, 20, 2, 10, 4, 8, 2, 2, 8, 2, 4, 4, 10, 2, 4, 10, 2, 2, 2, 10, 8, 20, 4, 2, 2, 10, 2, 2, 10, 4, 2, 2, 4, 20, 4, 14, 22, 4, 20, 4, 2, 2, 2, 10, 8, 4, 10, 8, 4, 2, 10, 16, 2, 8, 14, 4, 10, 8, 16, 8, 2, 2
Offset: 1

Views

Author

Zak Seidov, Nov 18 2005

Keywords

Comments

Other cases: k=1 A001223 Differences between consecutive primes, k=2 A059787, k=3 A114245, k=4 A114246, k=5 A114247, k=6 A114248, k=7 A111739, k=8 A111740, k=10 A111742.

Examples

			a(1)=1 because prime(1)=2 and 9*2+1=19 (prime).

Crossrefs

Cf. A001223, A059787, A114245, A114246, A114247, A114248, A111739, A111740, A111742.

A111742 Distance between k*(n-th prime) and next prime, k=10 case.

Original entry on oeis.org

3, 1, 3, 1, 3, 1, 3, 1, 3, 3, 1, 3, 9, 1, 9, 11, 3, 3, 3, 9, 3, 7, 9, 17, 1, 3, 1, 17, 1, 21, 7, 9, 3, 9, 3, 1, 1, 7, 23, 3, 11, 1, 3, 1, 3, 3, 1, 7, 3, 3, 3, 3, 1, 11, 9, 3, 3, 1, 7, 9, 3, 9, 9, 9, 7, 11, 3, 1, 21, 1, 3, 3, 1, 3, 3, 3, 17, 19, 3, 1, 11, 1, 17, 7, 1, 11, 3, 13, 11, 7, 3, 3, 1, 9, 3, 9, 9
Offset: 1

Views

Author

Zak Seidov, Nov 18 2005

Keywords

Comments

Other cases: k=1 A001223 Differences between consecutive primes, k=2 A059787, k=3 A114245, k=4 A114246, k=5 A114247, k=6 A114248, k=7 A111739, k=8 A111740, k=9 A111741.

Examples

			a(1)=3 because prime(1)=2 and 10*2+3=23 (prime).

Crossrefs

Cf. A001223, A059787, A114245, A114246, A114247, A114248, A111739, A111740, A111741.

A114247 Number of Fermat pseudoprimes to base 5 less than 10^n.

Original entry on oeis.org

1, 1, 5, 20, 73, 248, 745, 1954, 5239, 13837, 36042, 92893
Offset: 1

Views

Author

Eric W. Weisstein, Nov 18 2005

Keywords

Links

Crossrefs

Cf. A005936, A114245, A114249.

Programs

  • Mathematica
    Table[Count[Select[Range[2, 10^6], ! PrimeQ[#] && PowerMod[5, # - 1, #] == 1 &], x_ /; x < 10^n], {n, 6}]  (* Robert Price, Jun 09 2019 *)

Extensions

a(9)-a(12) from Hiroaki Yamanouchi, Sep 25 2015

A114249 Number of Fermat pseudoprimes to base 7 less than 10^n.

Original entry on oeis.org

1, 2, 6, 16, 73, 234, 659, 1797, 4950, 13070, 33989, 87448
Offset: 1

Views

Author

Eric W. Weisstein, Nov 18 2005

Keywords

Links

Crossrefs

Cf. A005938, A055550, A114245, A114247.

Programs

  • Mathematica
    Table[Count[Select[Range[2, 10^6], ! PrimeQ[#] && PowerMod[7, # - 1, #] == 1 &], x_ /; x < 10^n], {n, 6}]  (* Robert Price, Jun 09 2019 *)

Extensions

a(9)-a(12) from Hiroaki Yamanouchi, Sep 25 2015

A185084 Number of Fermat pseudoprimes to base 3 less than 2^n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 2, 2, 3, 6, 10, 17, 21, 30, 44, 61, 87, 124, 175, 254, 362, 511, 696, 955, 1313, 1802, 2462, 3321, 4422, 5969, 8089, 10785, 14513, 19333, 25774, 34259, 45522
Offset: 1

Views

Author

Washington Bomfim, Mar 02 2012

Keywords

Examples

			a(1) = a(2) = ... = a(6) = 0 because A005935(1) = 91 > 2^6.
a(7) = 2 since A005935(1) = 91, A005935(2) = 121, A005935(3) = 286, and 121 < 2^7 < 286.

Crossrefs

Cf. A005935, A114245.

Programs

  • Mathematica
    cnt = 0; Table[Do[If[! PrimeQ[i] && PowerMod[3, i-1, i] == 1, cnt++], {i, 2^(n-1) + 1, 2^n}]; cnt, {n, 20}] (* T. D. Noe, Mar 02 2012 *)

Extensions

a(35)-a(37) from Amiram Eldar, Jul 18 2021
Showing 1-7 of 7 results.

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