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.

A231626 Smallest sets of 5 consecutive deficient numbers in arithmetic progression. The initial deficient number is listed.

Original entry on oeis.org

1, 7, 13, 31, 43, 49, 61, 73, 91, 115, 121, 127, 133, 145, 151, 163, 169, 181, 187, 211, 229, 235, 241, 247, 253, 265, 283, 289, 295, 313, 325, 331, 343, 347, 355, 373, 385, 403, 409, 421, 427, 433, 451, 469, 481, 505, 511, 523, 535, 553, 565, 583, 589, 595
Offset: 1

Views

Author

Shyam Sunder Gupta, Nov 11 2013

Keywords

Examples

			1, 2, 3, 4, 5 is the smallest set of 5 consecutive deficient numbers in arithmetic progression so 1 is in the list.

Links

Crossrefs

Cf. A005100, A231623, A228962, A231624, A231625.

Programs

  • Mathematica
    DefQ[n_] := DivisorSigma[1, n] < 2 n; m = 2; z1 = 2; cd = 1; a = {}; Do[If[DefQ[n], If[n - z1 == cd, m = m + 1; If[m > 4, AppendTo[a, n - 4*cd]], m = 2; cd = n - z1]; z1 = n], {n, 3, 1000000}]; a

A231624 Smallest sets of 3 consecutive deficient numbers in arithmetic progression. The initial deficient number is listed.

Original entry on oeis.org

1, 2, 3, 7, 8, 9, 13, 14, 15, 17, 21, 25, 27, 31, 32, 33, 37, 39, 43, 44, 45, 49, 50, 51, 53, 57, 61, 62, 63, 67, 69, 73, 74, 75, 77, 81, 85, 87, 91, 92, 93, 97, 99, 101, 105, 109, 111, 115, 116, 117, 121, 122, 123, 127, 128, 129, 133, 134, 135, 137, 141
Offset: 1

Views

Author

Shyam Sunder Gupta, Nov 11 2013

Keywords

Examples

			1, 2, 3 is the smallest set of 3 consecutive deficient numbers in arithmetic progression so 1 is in the list.

Links

Crossrefs

Cf. A005100, A231623, A228844.

Programs

  • Mathematica
    DefQ[n_] := DivisorSigma[1, n] < 2 n; m = 2; z1 = 2; cd = 1; a = {}; Do[If[DefQ[n], If[n - z1 == cd, m = m + 1; If[m > 2, AppendTo[a, n - 2*cd]], m = 2; cd = n - z1]; z1 = n], {n, 3, 1000000}]; a

A231625 Smallest sets of 4 consecutive deficient numbers in arithmetic progression. The initial deficient number is listed.

Original entry on oeis.org

1, 2, 7, 8, 13, 14, 31, 32, 43, 44, 49, 50, 61, 62, 73, 74, 91, 92, 99, 115, 116, 121, 122, 127, 128, 133, 134, 145, 146, 151, 152, 163, 164, 169, 170, 181, 182, 187, 188, 195, 211, 212, 219, 229, 230, 235, 236, 241, 242, 247, 248, 253, 254, 265, 266, 283
Offset: 1

Views

Author

Shyam Sunder Gupta, Nov 11 2013

Keywords

Examples

			1, 2, 3, 4 is the smallest set of 4 consecutive deficient numbers in arithmetic progression so 1 is in the list.

Links

Crossrefs

Cf. A005100, A231623, A228961, A231624.

Programs

  • Mathematica
    DefQ[n_] := DivisorSigma[1, n] < 2 n; m = 2; z1 = 2; cd = 1; a = {}; Do[If[DefQ[n], If[n - z1 == cd, m = m + 1; If[m > 3, AppendTo[a, n - 3*cd]], m = 2; cd = n - z1]; z1 = n], {n, 3, 1000000}]; a

A231628 Smallest sets of 6 consecutive deficient numbers in arithmetic progression. The initial deficient number is listed.

Original entry on oeis.org

2987, 4727, 9723, 18843, 22983, 30543, 35147, 39947, 45047, 50463, 55787, 56807, 58055, 58779, 69183, 78047, 81947, 85743, 101147, 106143, 108255, 109247, 117123, 134087, 139743, 139803, 152567, 171287, 174347, 175907, 182643, 189767, 197027, 199803, 202127
Offset: 1

Views

Author

Shyam Sunder Gupta, Nov 11 2013

Keywords

Examples

			2987, 2989, 2991, 2993, 2995, 2997 is the smallest set of 6 consecutive deficient numbers in arithmetic progression so 2987 is in the list.

Links

Crossrefs

Cf. A005100, A231623, A228963, A231624, A231625, A231626.

Programs

  • Mathematica
    DefQ[n_] := DivisorSigma[1, n] < 2 n; m = 2; z1 = 2; cd = 1; a = {}; Do[If[DefQ[n], If[n - z1 == cd, m = m + 1; If[m > 5, AppendTo[a, n - 5*cd]], m = 2; cd = n - z1]; z1 = n], {n, 3, 1000000}]; a

A231629 First of 7 consecutive deficient numbers in arithmetic progression.

Original entry on oeis.org

801339, 962649, 7353339, 21964299, 41642139, 48049689, 55455939, 89034939, 89851449, 92253849, 105259539, 107948379, 109455339, 114295449, 116754939, 122349369, 135575979, 156009849, 159521049, 173645439, 188586699, 192674169, 193137849, 220301769, 221355125
Offset: 1

Views

Author

Shyam Sunder Gupta, Nov 11 2013

Keywords

Examples

			801339, 801341, 801343, 801345, 801347, 801349, 801351 is the smallest set of 7 consecutive deficient numbers in arithmetic progression so 801339 is in the list.

Links

Crossrefs

Cf. A005100, A231623, A228964, A231624, A231625, A231626, A231628.

Programs

  • Mathematica
    DefQ[n_] := DivisorSigma[1, n] < 2 n; m = 2; z1 = 2; cd = 1; a = {}; Do[If[DefQ[n], If[n - z1 == cd, m = m + 1; If[m > 6, AppendTo[a, n - 6*cd]], m = 2; cd = n - z1]; z1 = n], {n, 3, 1000000000}]; a

A350005 a(n) is the smallest number that starts an arithmetic progression of n consecutive ludic numbers (A003309), or 0 if no such number exists.

Original entry on oeis.org

1, 1, 1, 71, 6392047
Offset: 1

Views

Author

Pontus von Brömssen, Dec 08 2021

Keywords

Comments

a(n) is the smallest ludic number A003309(k), such that A260723(k) = A260723(k+1) = ... = A260723(k+n-2).
a(6) > 10^8 (unless a(6) = 0).

Examples

			The first arithmetic progression of 3 consecutive ludic numbers is (1, 2, 3), so a(3) = 1.
The first arithmetic progression of 4 consecutive ludic numbers is (71, 77, 83, 89), so a(4) = 71.
The first arithmetic progression of 5 consecutive ludic numbers is (6392047, 6392077, 6392107, 6392137, 6392167), so a(5) = 6392047.

Crossrefs

From n = 3, first row of A350007.
Cf. A003309, A260723.
Counterparts for other sequences than ludic numbers: A006560 (primes), A228433 (abundant numbers), A231623 (deficient numbers), A276821 (Sophie Germain primes), A330362 (lucky numbers).

A231630 Smallest sets of 8 consecutive deficient numbers in arithmetic progression. The initial deficient number is listed.

Original entry on oeis.org

221355125, 221355127, 402640539, 402640541, 668862579, 668862581, 739577139, 739577141
Offset: 1

Views

Author

Shyam Sunder Gupta, Nov 11 2013

Keywords

Examples

			221355125, 221355127, 221355129, 221355131, 221355133, 221355135, 221355137, 221355139 is the smallest set of 8 consecutive deficient numbers in arithmetic progression so 221355125 is in the list.

Crossrefs

Cf. A005100, A231623, A228965, A231624, A231625, A231626, A231628, A231629.

Programs

  • Mathematica
    DefQ[n_] := DivisorSigma[1, n] < 2 n; m = 2; z1 = 2; cd = 1; a = {}; Do[If[DefQ[n], If[n - z1 == cd, m = m + 1; If[m > 7, AppendTo[a, n - 7*cd]], m = 2; cd = n - z1]; z1 = n], {n, 3, 1000000000}]; a
Showing 1-7 of 7 results.

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