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.

Previous Showing 21-26 of 26 results.

A364126 Starts of runs of 4 consecutive integers that are Stolarsky-Niven numbers (A364123).

Original entry on oeis.org

125340, 945591, 14998632, 16160505, 19304934, 42053801, 42064137, 46049955, 57180537, 103562368, 108489885, 122495982, 135562299, 139343337, 147991452, 164002374, 271566942, 296019657, 301748706, 310980030, 314537247, 316725570, 333478935, 336959907, 349815255
Offset: 1

Views

Author

Amiram Eldar, Jul 07 2023

Keywords

Comments

Are there runs of 5 or more consecutive integers that are Stolarsky-Niven numbers?

Links

Crossrefs

Subsequence of A364123, A364124 and A364125.
Similar sequences: A141769, A328211, A328207, A328215, A330933, A331824, A334311, A342429, A344344, A352092, A352110, A352345, A352511.

Programs

  • Mathematica
    seq[2, 4] (* generates the first 2 terms, using the function seq[count, nConsec] from A364124 *)
  • PARI
    lista(2, 4) \\ generates the first 2 terms, using the function lista(count, nConsec) from A364124

A334372 Starts of runs of 4 consecutive Moran numbers (A001101).

Original entry on oeis.org

21481224, 22314620, 25502420, 25502421, 32432425, 130062260, 147026913, 713021425, 922216713, 938710112, 1012101135, 1019292153, 1113068913, 1420791155, 1545743565, 1671500190, 1805406154, 1941702882, 2010317425, 2027025025, 2200277555, 2307662313, 2437253313
Offset: 1

Views

Author

Amiram Eldar, Apr 25 2020

Keywords

Examples

			21481224 is a term since 21481224/(2+1+4+8+1+2+2+4) = 895051, 21481225/(2+1+4+8+1+2+2+5) = 859249, 21481226/(2+1+4+8+1+2+2+6) = 826201 and 21481227/(2+1+4+8+1+2+2+7) = 795601 are all primes.

Links

Crossrefs

Subsequence of A001101, A085775, A141769 and A334371.
Cf. A235397.

Programs

  • Mathematica
    moranQ[n_] := PrimeQ[n / Plus @@ IntegerDigits[n]]; m = moranQ /@ Range[4]; seq = {}; Do[If[And @@ m, AppendTo[seq, k - 4]]; m = Join[Rest[m], {moranQ[k]}], {k, 5, 3 * 10^7}]; seq

A364009 Starts of runs of 4 consecutive integers that are Wythoff-Niven numbers (A364006).

Original entry on oeis.org

374, 978, 17708, 832037, 1631097, 4821894, 5572377, 13376142, 14808759, 14930343, 35406720, 36534357, 38208519, 38748444, 38890509, 39088166, 65375232, 70046899, 79988116, 81224637, 82071105, 82898100, 94109430, 94875417, 95070492, 98014500, 100350522, 101651787, 102190437
Offset: 1

Views

Author

Amiram Eldar, Jul 01 2023

Keywords

Comments

Are there runs of 5 or more consecutive integers that are Wythoff-Niven numbers?

Crossrefs

Subsequence of A364006, A364007 and A364008.
Similar sequences: A141769, A328211, A328207, A328215, A330933, A331824, A334311, A342429, A344344, A352092, A352110, A352345, A352511.

Programs

  • Mathematica
    seq[3, 4] (* generates the first 3 terms using the function seq[count, nConsec] from A364007 *)

A331825 Positive numbers k such that -k, -(k + 1), -(k + 2), and -(k + 3) are 4 consecutive negative negabinary-Niven numbers (A331728).

Original entry on oeis.org

413, 2093, 3773, 4613, 7133, 7973, 8813, 10493, 11869, 15829, 16373, 23749, 30653, 31493, 34853, 35629, 37373, 39589, 40733, 49133, 51469, 54585, 55429, 63349, 64253, 65513, 67613, 70965, 75229, 91069, 98989, 102949, 103725, 106909, 110869, 114653, 129773, 131033
Offset: 1

Views

Author

Amiram Eldar, Jan 27 2020

Keywords

Links

Crossrefs

Cf. A027615, A039724, A141769, A328211, A328215, A330933, A331728, A331824.

Programs

  • Mathematica
    negaBinWt[n_] := negaBinWt[n] = If[n == 0, 0, negaBinWt[Quotient[n - 1, -2]] + Mod[n, 2]]; negaBinNivenQ[n_] := Divisible[n, negaBinWt[-n]]; nConsec = 4; neg = negaBinNivenQ /@ Range[nConsec]; seq = {}; c = 0; k = nConsec+1; While[c < 45, If[And @@ neg, c++; AppendTo[seq, k - nConsec]]; neg = Join[Rest[neg], {negaBinNivenQ[k]}]; k++]; seq

A338516 Starts of runs of 4 consecutive numbers that are divisible by the total binary weight of their divisors (A093653).

Original entry on oeis.org

1377595575, 4275143301, 13616091683, 13640596128, 15016388244, 15176619135, 21361749754, 23605084359, 24794290167, 28025464183, 29639590888, 30739547718, 33924433023, 35259630279, 38008366692, 38670247670, 38681191672, 40210059079, 40507412213, 49759198333, 52555068607
Offset: 1

Views

Author

Amiram Eldar, Oct 31 2020

Keywords

Comments

Can 5 consecutive numbers be divisible by the total binary weight of their divisors? If they exist, then they are larger than 10^11.

Examples

			1377595575 is a term since the 4 consecutive numbers from 1377595575 to 1377595578 are all terms of A093705.

Crossrefs

Subsequence of A338514 and A338515.
Cf. A000120, A093653, A093705.
Similar sequences: A141769, A330933, A334372, A338454.

Programs

  • Mathematica
    divQ[n_] := Divisible[n, DivisorSum[n, DigitCount[#, 2, 1] &]]; div = divQ /@ Range[4]; Reap[Do[If[And @@ div, Sow[k - 4]]; div = Join[Rest[div], {divQ[k]}], {k, 5, 5*10^9}]][[2, 1]]
SequencePosition[Table[If[Mod[n,Total[Flatten[IntegerDigits[#,2]&/@Divisors[n]]]]==0,1,0],{n,526*10^8}],{1,1,1,1}][[;;,1]] (* The program will take a long time to run. *) (* Harvey P. Dale, May 28 2023 *)

A359839 Numbers k such that k, k + 1 and k + 2 are 3 consecutive Niven (Harshad) numbers that are also divisible by a square.

Original entry on oeis.org

2023, 4912, 12103, 17575, 23273, 51424, 52675, 60399, 78650, 80800, 87723, 93624, 100303, 112624, 117962, 121224, 122875, 182182, 193075, 200752, 228175, 235024, 245725, 245726, 249500, 263275, 306963, 320704, 333475, 373490, 403675, 416583, 421072, 444624, 448000
Offset: 1

Views

Author

Bernard Schott, Jan 15 2023

Keywords

Comments

Equivalently, smallest of 3 consecutive numbers each divisible by a square and also divisible by the sum of their digits (Niven numbers).

Examples

			2023 = 7 * 17^2 = 289 * (2+0+2+3); 2024 = 506 * 2^2 = 253 * (2+0+2+4) and 2025 = 81 * 5^2 = 225 * (2+0+2+5) hence 2023 is a term.

References

  • Jean-Marie De Koninck, Ces nombres qui nous fascinent, Entry 48, p. 18, Ellipses, Paris, 2008.
  • Jean-Marie De Koninck, Those Fascinating Numbers, Entry 110, p. 36, American Mathematical Society, 2009.

Links

Crossrefs

Intersection of A070258 and A154701.
Cf. A013929, A068781, A235578.
Cf. A005349, A060159, A141769, A330927, A330928, A330929, A330930.

Programs

  • Mathematica
    q[n_] := Divisible[n, Total@IntegerDigits[n]] && ! SquareFreeQ[n]; tri = q /@ Range[3]; seq = {}; Do[tri = Join[Rest[tri], {q[k]}]; If[And @@ tri, AppendTo[seq, k - 2]], {k, 3, 5*10^5}]; seq (* Amiram Eldar, Jan 15 2023 *)

Extensions

More terms from Amiram Eldar, Jan 15 2023
Previous Showing 21-26 of 26 results.

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

Content is available under The OEIS End-User License Agreement.