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.

A352508 Catalan-Niven numbers: numbers that are divisible by the sum of the digits in their representation in terms of the Catalan numbers (A014418).

Original entry on oeis.org

1, 2, 4, 5, 6, 9, 10, 12, 14, 16, 18, 21, 24, 28, 30, 32, 33, 40, 42, 44, 45, 48, 55, 56, 57, 60, 65, 72, 78, 80, 84, 88, 95, 100, 105, 112, 126, 128, 130, 132, 134, 135, 138, 140, 144, 145, 146, 147, 152, 155, 156, 168, 170, 174, 180, 184, 185, 195, 210, 216
Offset: 1

Views

Author

Amiram Eldar, Mar 19 2022

Keywords

Comments

Numbers k such that A014420(k) | k.
All the Catalan numbers (A000108) are terms.
If k is an odd Catalan number (A038003), then k+1 is a term.

Examples

			4 is a term since its Catalan representation, A014418(4) = 20, has the sum of digits A014420(4) = 2 + 0 = 2 and 4 is divisible by 2.
9 is a term since its Catalan representation, A014418(9) = 120, has the sum of digits A014420(9) = 1 + 2 + 0 = 3 and 9 is divisible by 3.

Links

Crossrefs

Cf. A014418, A014420.
Subsequences: A000108, A038003, A352509, A352510, A352511.
Similar sequences: A005349, A049445, A064150, A064438, A064481, A118363, A328208, A328212, A331085, A333426, A342726, A334308, A331728, A342426, A344341, A351714, A351719, A352089, A352107, A352320, A352342.

Programs

  • Mathematica
    c[n_] := c[n] = CatalanNumber[n]; q[n_] := Module[{s = {}, m = n, i}, While[m > 0, i = 1; While[c[i] <= m, i++]; i--; m -= c[i]; AppendTo[s, i]]; Divisible[n, Plus @@ IntegerDigits[Total[4^(s - 1)], 4]]]; Select[Range[216], q]

A352509 Numbers k such that k and k+1 are both Catalan-Niven numbers (A352508).

Original entry on oeis.org

1, 4, 5, 9, 32, 44, 55, 56, 134, 144, 145, 146, 155, 184, 234, 324, 329, 414, 426, 429, 434, 455, 511, 512, 603, 636, 930, 1004, 1014, 1160, 1183, 1215, 1287, 1308, 1448, 1472, 1505, 1562, 1595, 1808, 1854, 1967, 1985, 1995, 2051, 2075, 2096, 2135, 2165, 2255
Offset: 1

Views

Author

Amiram Eldar, Mar 19 2022

Keywords

Examples

			4 is a term since 4 and 5 are both Catalan-Niven numbers: the Catalan representation of 4, A014418(20) = 20, has the sum of digits 2+0 = 2 and 4 is divisible by 2, and the Catalan representation of 5, A014418(5) = 100, has the sum of digits 1+0+0 = 1 and 5 is divisible by 1.

Links

Crossrefs

Cf. A000108, A014418, A014420.
Subsequence of A352508.
Subsequences: A038003, A352510, A352511.
Similar sequences: A330927, A328205, A328209, A328213, A330931, A331086, A333427, A334309, A331820, A342427, A344342, A351715, A351720, A352090, A352108, A352321, A352343.

Programs

  • Mathematica
    c[n_] := c[n] = CatalanNumber[n]; q[n_] := Module[{s = {}, m = n, i}, While[m > 0, i = 1; While[c[i] <= m, i++]; i--; m -= c[i]; AppendTo[s, i]]; Divisible[n, Plus @@ IntegerDigits[Total[4^(s - 1)], 4]]]; Select[Range[2300], q[#] && q[#+1] &]

A352510 Starts of runs of 3 consecutive Catalan-Niven numbers (A352508).

Original entry on oeis.org

4, 55, 144, 145, 511, 2943, 6950, 7734, 9470, 9750, 15630, 15631, 35034, 35464, 41590, 41986, 64735, 68523, 68870, 77510, 81150, 90958, 106063, 118264, 119043, 135970, 139403, 163188, 164862, 164863, 171346, 181510, 200759, 202761, 202762, 208024, 209230, 209586
Offset: 1

Views

Author

Amiram Eldar, Mar 19 2022

Keywords

Examples

			4 is a term since 4, 5 and 6 are all Catalan-Niven numbers: the Catalan representation of 4, A014418(20) = 20, has the sum of digits 2+0 = 2 and 4 is divisible by 2, the Catalan representation of 5, A014418(5) = 100, has the sum of digits 1+0+0 = 1 and 5 is divisible by 1, and the Catalan representation of 6, A014418(6) = 101, has the sum of digits 1+0+1 = 2 and 6 is divisible by 2.

Links

Crossrefs

Cf. A000108, A014418, A014420.
Subsequence of A352508 and A352509.
A352511 is a subsequence.
Similar sequences: A154701, A328206, A328210, A328214, A330932, A331087, A333428, A334310, A331822, A342428, A344343, A351716, A351721, A352091, A352109, A352322, A352344.

Programs

  • Mathematica
    c[n_] := c[n] = CatalanNumber[n]; catNivQ[n_] := Module[{s = {}, m = n, i}, While[m > 0, i = 1; While[c[i] <= m, i++]; i--; m -= c[i]; AppendTo[s, i]]; Divisible[n, Plus @@ IntegerDigits[Total[4^(s - 1)], 4]]]; seq[count_, nConsec_] := Module[{cn = catNivQ /@ Range[nConsec], s = {}, c = 0, k = nConsec + 1}, While[c < count, If[And @@ cn, c++; AppendTo[s, k - nConsec]]; cn = Join[Rest[cn], {catNivQ[k]}]; k++]; s]; seq[30, 3]

A364219 Starts of runs of 4 consecutive integers that are Jacobsthal-Niven numbers (A364216).

Original entry on oeis.org

1, 42, 43, 2731, 11605, 13024, 14229, 25983, 39390, 45727, 46624, 47529, 60073, 96039, 111390, 131103, 132010, 133984, 134430, 140767, 148180, 148181, 148509, 174762, 174763, 187744, 197790, 237609, 247114, 266453, 275229, 287988, 312190, 330847, 354429, 370269
Offset: 1

Views

Author

Amiram Eldar, Jul 14 2023

Keywords

Links

Crossrefs

Subsequence of A364216, A364217 and A364218.
Subsequences: A364220, A364221.
Similar sequences: A141769, A328211, A328207, A328215, A330933, A331824, A334311, A342429, A344344, A352092, A352110, A352345, A352511.

Programs

  • Mathematica
    consecJacobsthalNiven[4*10^5, 4] (* using the function from A364217 *)
  • PARI
    lista(4*10^5, 4) \\ using the function from A364217

A364382 Starts of runs of 4 consecutive integers that are greedy Jacobsthal-Niven numbers (A364379).

Original entry on oeis.org

1, 2, 3, 8, 9, 42, 43, 84, 85, 2730, 2731, 5460, 5461, 21864, 21865, 59477, 60073, 66303, 75048, 112509, 156607, 174762, 174763, 283327, 312190, 320768, 349524, 349525, 351570, 354429, 374589, 384039, 479037, 504510, 527103, 624040, 625470, 656829, 688830, 711423
Offset: 1

Views

Author

Amiram Eldar, Jul 21 2023

Keywords

Links

Crossrefs

Cf. A265745, A265747.
Subsequence of A364379, A364380 and A364381.
A364383 is a subsequence.
Similar sequences: A141769, A328211, A328207, A328215, A330933, A331824, A334311, A342429, A344344, A352092, A352110, A352345, A352511, A364219.

Programs

  • Mathematica
    consecGreedyJN[72000, 4] (* using the function consecGreedyJN from A364380 *)
  • PARI
    lista(10^5, 4) \\ using the function lista from A364380

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

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 *)
Showing 1-7 of 7 results.

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

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