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 1-3 of 3 results.

A248590 Least positive integer m such that prime(m) == 1 (mod m + n).

Original entry on oeis.org

3, 4, 19, 10, 5, 6, 13, 15, 7, 8, 31, 17, 9, 19, 20, 38, 22, 10, 11, 24, 78, 80, 25, 12, 28, 30, 13, 14, 599, 97, 15, 31, 32, 178, 33, 16, 102, 104, 35, 108, 17, 18, 38, 39, 361, 40, 19, 41, 73, 20, 21, 43, 45, 78, 134, 22, 391, 47, 23, 84
Offset: 1

Views

Author

Zhi-Wei Sun, Oct 09 2014

Keywords

Comments

Conjecture: (i) a(n) exists for any n > 0. Moreover, a(n) < n*(n-1) if n > 3.
(ii) For any n > 0, there is a positive integer m such that prime(m) == -1 (mod m + n). Moreover, we may require m < n*(n-1) if n > 1.

Examples

			a(3) = 19 since prime(19) = 67 == 1 (mod 19 + 3).

Links

Crossrefs

Cf. A000040, A247824, A248004, A248588.

Programs

  • Mathematica
    Do[m=1;Label[aa];If[Mod[Prime[m]-1,m+n]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,60}]

A248593 Least positive integer m such that m + n divides F(m), where F(m) is the m-th Fibonacci number given by A000045.

Original entry on oeis.org

10, 6, 84, 12, 16, 7, 27, 9, 144, 30, 28, 12, 8, 30, 14, 18, 57, 19, 342, 18, 20, 24, 66, 12, 9, 27, 144, 60, 112, 35, 16, 24, 60, 55, 20, 12, 40, 111, 24, 36, 88, 72, 80, 48, 10, 15, 72, 24, 224, 18, 50, 54, 270, 72, 54, 33, 224, 18, 28, 12
Offset: 1

Views

Author

Zhi-Wei Sun, Oct 09 2014

Keywords

Comments

Conjecture: a(n) exists for any n > 0. Moreover, a(n) <= n*(n-1) except for n = 1, 2, 3, 9.
In contrast, it is easy to show that for any integer n > 0, there is a positive integer m such that m + n divides 2^m - 1.
a(n) exists for any n > 0. See Bloom (1998). - Amiram Eldar, Jan 15 2022

Examples

			a(1) = 10 since 10 + 1 = 11 divides F(10) = 55.

Links

Crossrefs

Cf. A000045, A247937, A247940, A248588, A248590.

Programs

  • Mathematica
    Do[m=1;Label[aa];If[Mod[Fibonacci[m],m+n]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,60}]

A248626 Least positive integer m such that prime(m+n) divides 2^m - 1.

Original entry on oeis.org

3, 22, 18, 50, 48, 5, 48, 121, 390, 21, 37, 9, 11, 110, 672, 11628, 14, 286, 1000, 329, 15, 29, 32, 7, 90, 42, 1001, 816, 24, 408, 806, 6219, 761, 44, 75, 88, 30, 711, 16, 43, 2202, 110, 6112, 624, 12206, 590, 21, 156, 551, 525, 194, 64, 201, 225, 261, 1132, 305, 66, 500, 50
Offset: 1

Views

Author

Zhi-Wei Sun, Oct 10 2014

Keywords

Comments

Conjecture: a(n) exists for any n > 0.

Examples

			a(2) = 22 since prime(22+2) = 89 divides 2^(22)-1 = 4194303 = 89*47127.

Links

Crossrefs

Cf. A000040, A000225, A248588.

Programs

  • Mathematica
    Do[m=1;Label[aa];If[Mod[2^m-1,Prime[m+n]]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,60}]
Showing 1-3 of 3 results.

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

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