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 1-6 of 6 results.

A364220 Starts of runs of 5 consecutive integers that are Jacobsthal-Niven numbers (A364216).

Original entry on oeis.org

42, 148180, 174762, 2366376, 2809300, 3758676, 3938856, 4463016, 4987176, 6559656, 6817149, 11975380, 12325416, 12849576, 13029756, 13373736, 15470376, 17567016, 18271356, 23332776, 23512956, 24037116, 24561276, 25953576, 26657916, 27974439, 28754556, 28754557
Offset: 1

Views

Author

Amiram Eldar, Jul 14 2023

Keywords

Crossrefs

Subsequence of A364216, A364217, A364218 and A364219.
A364221 is a subsequence.
Cf. A330928.

Programs

  • Mathematica
    consecJacobsthalNiven[4*10^5, 5] (* using the function from A364217 *)
  • PARI
    lista(3*10^6, 5) \\ using the function from A364217

A364216 Jacobsthal-Niven numbers: numbers that are divisible by the sum of the digits in their Jacobsthal representation (A280049).

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 9, 11, 12, 14, 15, 16, 20, 22, 24, 27, 28, 32, 33, 36, 40, 42, 43, 44, 45, 46, 48, 51, 52, 54, 56, 57, 60, 68, 72, 75, 76, 84, 86, 87, 88, 92, 93, 95, 96, 99, 100, 104, 105, 108, 112, 115, 117, 120, 125, 126, 128, 129, 132, 135, 136, 138, 140
Offset: 1

Views

Author

Amiram Eldar, Jul 14 2023

Keywords

Comments

Numbers k such that A364215(k) | k.
A007583 is a subsequence since A364215(A007583(n)) = 1 for n >= 0.

Crossrefs

Programs

  • Mathematica
    seq[kmax_] := Module[{m = 1, s = {}}, Do[If[Divisible[k, DigitCount[m, 2, 1]], AppendTo[s, k]]; While[m++; OddQ[IntegerExponent[m, 2]]], {k, 1, kmax}]; s]; seq[140]
  • PARI
    lista(kmax) = {my(m = 1); for(k = 1, kmax, if( !(k % sumdigits(m, 2)), print1(k,", ")); until(valuation(m, 2)%2 == 0, m++));}

A364217 Numbers k such that k and k+1 are both Jacobsthal-Niven numbers (A364216).

Original entry on oeis.org

1, 2, 3, 8, 11, 14, 15, 27, 32, 42, 43, 44, 45, 51, 56, 75, 86, 87, 92, 95, 99, 104, 125, 128, 135, 144, 155, 171, 176, 182, 183, 195, 204, 264, 267, 275, 287, 305, 344, 363, 375, 387, 428, 444, 455, 474, 497, 512, 524, 535, 544, 545, 552, 555, 581, 605, 623, 639
Offset: 1

Views

Author

Amiram Eldar, Jul 14 2023

Keywords

Comments

A001045(2*n+1) = A007583(n) = (2^(2*n+1) + 1)/3 is a term for n >= 0, since its representation is 2*n 1's, so A364215(A001045(2*n+1)) = 1 divides A001045(2*n+1), and the representation of A001045(2*n+1) + 1 = (2^(2*n+1) + 4)/3 is max(2*n-1, 0) 0's between 2 1's, so A364215(A001045(2*n+1) + 1) = 2 which divides (2^(2*n+1) + 4)/3.

Crossrefs

Programs

  • Mathematica
    consecJacobsthalNiven[kmax_, len_] := Module[{m = 1, c = Table[False, {len}], s = {}}, Do[c = Join[Rest[c], {Divisible[k, DigitCount[m, 2, 1]]}]; While[m++; OddQ[IntegerExponent[m, 2]]]; If[And @@ c, AppendTo[s, k - len + 1]], {k, 1, kmax}]; s]; consecJacobsthalNiven[640, 2]
  • PARI
    lista(kmax, len) = {my(m = 1, c = vector(len)); for(k = 1, kmax, c = concat(vecextract(c, "^1"), !(k % sumdigits(m, 2))); until(valuation(m, 2)%2 == 0, m++); if(vecsum(c) == len, print1(k-len+1, ", ")));}
    lista(640, 2)

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

Crossrefs

Subsequence of A364216, A364217 and A364218.
Subsequences: A364220, A364221.

Programs

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

A364221 Starts of runs of 6 consecutive integers that are Jacobsthal-Niven numbers (A364216).

Original entry on oeis.org

28754556, 103529256, 121576571, 288033576, 293979516, 414100179, 497440040, 584411859, 766411476, 858663636, 1498843176, 1591095336, 1637221416, 1683347496, 1775599656, 1816140156, 2341109715, 2789551400, 2882625576, 3042399699, 3044066856, 3067129896, 3240102696
Offset: 1

Views

Author

Amiram Eldar, Jul 14 2023

Keywords

Comments

Are there 7 or more consecutive integers that are Jacobsthal-Niven numbers?

Crossrefs

Subsequence of A364216, A364217, A364218, A364219 and A364220.
Cf. A330929.

Programs

  • Mathematica
    consecJacobsthalNiven[1.2*10^8, 6] (* using the function from A364217 *)
  • PARI
    lista(1.2*10^8, 6) \\ using the function from A364217

A364381 Starts of runs of 3 consecutive integers that are greedy Jacobsthal-Niven numbers (A364379).

Original entry on oeis.org

1, 2, 3, 4, 8, 9, 10, 14, 20, 26, 42, 43, 44, 84, 85, 86, 104, 115, 170, 182, 304, 344, 362, 414, 544, 682, 686, 692, 784, 854, 1014, 1370, 1384, 1504, 1673, 1685, 1706, 2224, 2315, 2358, 2730, 2731, 2732, 2763, 2774, 3243, 3594, 3702, 4144, 4688, 4864, 5046, 5408
Offset: 1

Views

Author

Amiram Eldar, Jul 21 2023

Keywords

Crossrefs

Programs

  • Mathematica
    consecGreedyJN[5500, 3] (* using the function consecGreedyJN from A364380 *)
  • PARI
    lista(5500, 3) \\ using the function lista from A364380
Showing 1-6 of 6 results.