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 1-4 of 4 results.

A364379 Greedy Jacobsthal-Niven numbers: numbers that are divisible by the sum of the digits in their representation in Jacobsthal greedy base (A265747).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 20, 21, 22, 24, 26, 27, 28, 32, 33, 36, 40, 42, 43, 44, 45, 46, 48, 51, 52, 54, 56, 57, 60, 64, 68, 69, 72, 75, 76, 80, 84, 85, 86, 87, 88, 90, 92, 93, 96, 99, 100, 104, 105, 106, 108, 111, 112, 115, 116, 117, 120
Offset: 1

Views

Author

Amiram Eldar, Jul 21 2023

Keywords

Comments

Numbers k such that A265745(k) | k.
The positive Jacobsthal numbers, A001045(n) for n >= 1, are terms since their representation in Jacobsthal greedy base is one 1 followed by n-1 0's, so A265745(A001045(n)) = 1 divides A001045(n).

Links

Crossrefs

Cf. A265745, A265747.
Subsequences: A364380, A364381, A364382, A364383.
Similar sequences: A005349, A049445, A064150, A064438, A064481, A118363, A328208, A328212, A331085, A333426, A342726, A334308, A331728, A342426, A344341, A351714, A351719, A352089, A352107, A352320, A352342, A352508, A364216.

Programs

  • Mathematica
    greedyJacobNivenQ[n_] := Divisible[n, A265745[n]]; Select[Range[120], greedyJacobNivenQ] (* using A265745[n] *)
  • PARI
    isA364379(n) = !(n % A265745(n)); \\ using A265745(n)

A364380 Numbers k such that k and k+1 are both greedy Jacobsthal-Niven numbers (A364379).

Original entry on oeis.org

1, 2, 3, 4, 5, 8, 9, 10, 11, 14, 15, 20, 21, 26, 27, 32, 42, 43, 44, 45, 51, 56, 68, 75, 84, 85, 86, 87, 92, 99, 104, 105, 111, 115, 116, 125, 128, 135, 144, 155, 170, 171, 176, 182, 183, 195, 204, 213, 219, 224, 260, 264, 267, 275, 304, 305, 324, 329, 341, 344
Offset: 1

Views

Author

Amiram Eldar, Jul 21 2023

Keywords

Comments

The positive Jacobsthal numbers, A001045(n) for n >= 1, are terms since their representation in Jacobsthal greedy base is one 1 followed by n-1 0's, so A265745(A001045(n)) = 1 divides A001045(n), and the representation of A001045(n) + 1 is 2 if n <= 2 and otherwise n-3 0's between two 1's, so A265745(A001045(n) + 1) = 2 which divides A001045(n) + 1.

Links

Crossrefs

Cf. A265745, A265747.
Subsequence of A364379.
Subsequences: A364381, A364382, A364383.
Similar sequences: A330927, A328205, A328209, A328213, A330931, A331086, A333427, A334309, A331820, A342427, A344342, A351715, A351720, A352090, A352108, A352321, A352343, A352509, A364217.

Programs

  • Mathematica
    consecGreedyJN[kmax_, len_] := Module[{m = 1, c = Table[False, {len}], s = {}}, Do[c = Join[Rest[c], {greedyJacobNivenQ[k]}]; If[And @@ c, AppendTo[s, k - len + 1]], {k, 1, kmax}]; s]; consecGreedyJN[350, 2] (* using the function greedyJacobNivenQ[n] from A364379 *)
  • PARI
    lista(kmax, len) = {my(c = vector(len)); for(k = 1, kmax, c = concat(vecextract(c, "^1"), isA364379(k)); if(vecsum(c) == len, print1(k-len+1, ", ")));} \\ using the function isA364379(n) from A364379
lista(350, 2)

A364383 Starts of runs of 5 consecutive integers that are greedy Jacobsthal-Niven numbers (A364379).

Original entry on oeis.org

1, 2, 8, 42, 84, 2730, 5460, 21864, 174762, 349524, 8575060, 11184810, 89478504, 106502227, 109295017, 181276927, 181843540, 184069717, 223830100, 245705471, 279956051, 280652201, 287571966, 291006547, 316295081, 316991231, 358660180, 360195667, 362988457, 422527571
Offset: 1

Views

Author

Amiram Eldar, Jul 21 2023

Keywords

Comments

Is 1 the only start of a run of 6 consecutive integers that are greedy Jacobsthal-Niven numbers?

Links

Crossrefs

Cf. A265745, A265747.
Subsequence of A364379, A364380, A364381 and A364382.
Similar sequences: A330928, A364220.

Programs

  • Mathematica
    consecGreedyJN[2*10^5, 5] (* using the function consecGreedyJN from A364380 *)
  • PARI
    lista(2*10^5, 5) \\ using the function lista from A364380

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
Showing 1-4 of 4 results.

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

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