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.

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.

Links

Crossrefs

Cf. A280049, A364215.
Subsequences: A007583, A364217, A364218, A364219, A364220, A364221.
Similar sequences: A005349, A049445, A064150, A064438, A064481, A118363, A328208, A328212, A331085, A333426, A342726, A334308, A331728, A342426, A344341, A351714, A351719, A352089, A352107, A352320, A352342, A352508.

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.

Links

Crossrefs

Cf. A364215.
Subsequence of A364216.
Subsequences: A364218, A364219, A364220, A364221.
Similar sequences: A330927, A328205, A328209, A328213, A330931, A331086, A333427, A334309, A331820, A342427, A344342, A351715, A351720, A352090, A352108, A352321, A352343, A352509.

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)

A364218 Starts of runs of 3 consecutive integers that are Jacobsthal-Niven numbers (A364216).

Original entry on oeis.org

1, 2, 14, 42, 43, 44, 86, 182, 544, 686, 846, 854, 1014, 1375, 1384, 1504, 1624, 2105, 2190, 2315, 2358, 2731, 2732, 2763, 2774, 2824, 3243, 3534, 3702, 4205, 4878, 5046, 5408, 5462, 5643, 5663, 6222, 6390, 6935, 7566, 7734, 7928, 8224, 8704, 8910, 9078, 9368
Offset: 1

Views

Author

Amiram Eldar, Jul 14 2023

Keywords

Links

Crossrefs

Subsequence of A364216 and A364217.
Subsequence of A364219, A364220, A364221.
Similar sequences: A154701, A328206, A328210, A328214, A330932, A331087, A333428, A334310, A331822, A342428, A344343, A351716, A351721, A352091, A352109, A352322, A352344, A352510.

Programs

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

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

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?

Links

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

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

A381585 Starts of runs of 5 consecutive integers that are all terms in A381581.

Original entry on oeis.org

57744971, 159104411, 203738652, 212548572, 260463851, 361823291, 413644572, 431577521, 440353328, 520800012, 717222337, 726300972, 779825648, 843559091, 913313321, 945016812, 986681527, 1091786528, 1116032201, 1185786431, 1318751081, 1347208812, 1360423692, 1418212627
Offset: 1

Views

Author

Amiram Eldar, Feb 28 2025

Keywords

Comments

Are there 6 consecutive integers that are all terms in A381581?

Examples

			57744971 is a term since A291711(57744971) = 17 divides 57744971, A291711(57744972) = 18 divides 57744972, A291711(57744973) = 13 divides 57744973, A291711(57744974) = 14 divides 57744974, and A291711(57744975) = 15 divides 57744975.

Links

Crossrefs

Cf. A291711.
Subsequence of A381581, A381582, A381583 and A381584.
Similar sequences: A330928, A334373, A364220, A364383.

Programs

  • PARI
    mx = 20; fvec = vector(mx, i, fibonacci(2*i)); f(n) = if(n <= mx, fvec[n], fibonacci(2*n));
is1(n) = {my(s = 0, m = n, k); while(m > 0, k = 1; while(m > f(k), k++); if(m < f(k), k--); if(m >= 2*f(k), s += 2; m -= 2*f(k), s++; m -= f(k))); !(n % s);}
list(lim) = {my(q1 = is1(1), q2 = is1(2), q3 = is1(3), q4 = is1(4), s5); for(k = 5, lim, q5 = is1(k); if(q1 && q2 && q3 && q4 && q5, print1(k-4, ", ")); q1 = q2; q2 = q3; q3 = q4; q4 = q5);}
Showing 1-7 of 7 results.

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

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