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.

A248136 Least positive integer m such that m + n divides D(m) + D(n), where D(.) is given by A001850.

Original entry on oeis.org

1, 20, 3, 6, 1, 4, 200, 299, 5, 29, 4, 119, 5, 61, 3, 3, 6, 64, 31, 2, 21, 35, 6, 2974, 17, 1052, 27, 109, 10, 4, 3, 50, 65, 177, 22, 29, 5, 25, 15, 29, 29, 584, 83, 163, 9, 152, 19, 19, 29, 32, 15, 35, 4, 25, 239, 1122, 185, 76, 35, 97
Offset: 1

Views

Author

Zhi-Wei Sun, Oct 02 2014

Keywords

Comments

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

Examples

			a(2) = 20 since 2 + 20 = 22 divides D(2) + D(20) = 13 + 260543813797441 = 260543813797454 = 22*11842900627157.

Links

Crossrefs

Cf. A001850, A247824, A247937, A247940, A248124, A248125, A248133, A248137, A248139, A248142.

Programs

  • Mathematica
    d[n_]:=Sum[Binomial[n,k]Binomial[n+k,k],{k,0,n}]
Do[m=1;Label[aa];If[Mod[d[m]+d[n],m+n]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,60}]

A248137 Least positive integer m such that m + n divides M(m) + M(n), where M(.) is given by A001006.

Original entry on oeis.org

1, 1, 244, 1, 23, 4, 1, 1, 3494, 1, 68058, 4, 20, 18, 35, 1, 4, 14, 32, 13, 21, 1, 5, 22, 172, 7, 8, 1, 1, 28, 14, 19, 2, 178, 15, 227, 2, 6, 109, 1, 22, 122, 47, 22, 126, 1, 43, 60, 41, 18, 24, 1, 13, 23, 21, 24, 126, 1, 152, 6
Offset: 1

Views

Author

Zhi-Wei Sun, Oct 02 2014

Keywords

Comments

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

Examples

			a(5) = 23 since 5 + 23 = 28 divides M(5) + M(23) = 21 + 1129760415 = 1129760436 = 28*40348587.

Links

Crossrefs

Cf. A001006, A247824, A247937, A247940, A248124, A248125, A248133, A248136, A248139, A248142.

Programs

  • Mathematica
    M[n_]:=Sum[Binomial[n,2k]Binomial[2k,k]/(k+1),{k,0,n/2}]
Do[m=1;Label[aa];If[Mod[M[m]+M[n],m+n]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,60}]

A248139 Least positive integer m such that m + n divides f(m) + f(n), where f(.) is given by A000172.

Original entry on oeis.org

1, 1, 25, 6, 14, 4, 13, 49, 19, 10, 2, 56, 2, 5, 6, 5, 27, 61, 9, 33, 23, 53, 21, 15, 3, 24, 11, 58, 39, 118, 3, 1598, 20, 40, 4, 2, 58, 26, 29, 17, 47, 34, 4, 31, 43, 163, 41, 25, 8, 26, 67, 40, 21, 214, 535, 12, 7, 22, 164, 74
Offset: 1

Views

Author

Zhi-Wei Sun, Oct 02 2014

Keywords

Comments

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

Examples

			a(5) = 14 since 5 + 14 = 19 divides f(5) + f(14) = 2252 + 112738423360 = 112738425612 = 19*5933601348.

Links

Crossrefs

Cf. A000172, A247824, A247937, A247940, A248124, A248125, A248133, A248136, A248137, A248142.

Programs

  • Mathematica
    f[n_]:=Sum[Binomial[n,k]^3,{k,0,n}]
Do[m=1; Label[aa]; If[Mod[f[m]+f[n], m+n]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}]

A248142 Least positive integer m such that m + n divides A(m) + A(n), where A(.) is given by A005259.

Original entry on oeis.org

1, 1, 7, 2238, 5, 9, 3, 3, 1, 2484, 2, 2, 26, 12, 24, 5, 41, 32, 14, 3, 29, 29, 6, 15, 30, 7, 8, 37, 21, 5, 44, 18, 5, 16, 39, 34, 8, 1, 6, 5, 17, 8, 26, 6, 865, 39, 8, 13, 16, 781, 356, 35, 184, 65, 30, 139, 18, 25, 16, 123
Offset: 1

Views

Author

Zhi-Wei Sun, Oct 02 2014

Keywords

Comments

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

Examples

			 a(3) = 7 since 3 + 7 = 10 divides A(3) + A(7) = 1445 + 584307365 = 584308810.

Links

Crossrefs

Cf. A005259, A247824, A247937, A247940, A248124, A248125, A248133, A248136, A248137, A248139.

Programs

  • Mathematica
    A[0]=1;A[1]=5
A[n_]:=((2n-1)(17*n(n-1)+5)*A[n-1]-(n-1)^3*A[n-2])/n^3
Do[m=1; Label[aa]; If[Mod[A[m]+A[n], m+n]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}]

A248143 Least integer m > 0 such that m + n divides p(m) + p(n), where p(.) is the partition function given by A000041.

Original entry on oeis.org

1, 1, 1, 61, 13, 7, 1, 25, 109, 41, 60, 1, 5, 24, 18, 6, 3, 7, 38, 12, 86, 31, 18, 14, 8, 96, 470, 2, 37, 245, 8, 6, 37, 2, 20, 137, 3, 19, 24, 63, 10, 99, 52, 32, 16, 638, 15, 20, 61, 45, 288, 43, 52, 12, 371, 123, 94, 8, 483, 11
Offset: 1

Views

Author

Zhi-Wei Sun, Oct 02 2014

Keywords

Comments

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

Examples

			a(5) = 13 since 5 + 13 = 18 divides p(5) + p(13) = 7 + 101 = 108.

Links

Crossrefs

Cf. A000041, A247824, A247937, A247940, A248124, A248125, A248133, A248136, A248137, A248139, A248142, A248144.

Programs

  • Mathematica
    Do[m=1;Label[aa];If[Mod[PartitionsP[m]+PartitionsP[n],m+n]==0,Print[n," ",m];Goto[bb]];m=m+1;Goto[aa];Label[bb];Continue,{n,1,60}]
Showing 1-5 of 5 results.

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