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.

A376794 Starts of runs of 3 consecutive integers that are in A376616.

Original entry on oeis.org

38143807, 67141710, 67511743, 67736383, 269912383, 675612223, 1251282942, 2216832254, 4135244542, 4213075438, 4256878846, 4608511334, 5089851270, 5148094783, 5383281343, 5457887279, 5905845439, 7247769919, 7355297535, 7811735295, 8209151742, 8503999231, 8591105023, 9015656767
Offset: 1

Views

Author

Amiram Eldar, Oct 04 2024

Keywords

Examples

			38143807 is a term since 38143807, 38143808 and 38143809 are all in A376616: 38143807/A000120(38143807) = 2934139, and 2934139/A000120(2934139) = 225703 are integers, 38143808/A000120(38143808) = 4767976, and 4767976/A000120(4767976) = 595997 are integers, and 38143809/A000120(38143809) = 4238201, and 4238201/A000120(4238201) = 385291 are integers.

Links

Crossrefs

Subsequence of A330932, A376616 and A376793.
Cf. A000120.

Programs

  • Mathematica
    q[k_] := q[k] = Module[{w = DigitCount[k, 2, 1]}, Divisible[k, w] && Divisible[k/w, DigitCount[k/w, 2, 1]]]; Select[Range[10^8], q[#] && q[#+1] && q[#+2] &]
  • PARI
    is1(k) = {my(w = hammingweight(k)); !(k % w) && !((k/w) % hammingweight(k/w));}
lista(kmax) = {my(q1 = is1(1), q2 = is1(2), q3); for(k = 3, kmax, q3 = is1(k); if(q1 && q2 && q3, print1(k-2, ", ")); q1 = q2; q2 = q3);}

A376795 Numbers k such that k and k+1 are both in A376617.

Original entry on oeis.org

1, 10624, 13824, 1114112, 2625664, 4563999, 6554624, 16843904, 17266688, 17368064, 20003840, 27137024, 32375160, 32679360, 42993664, 44643599, 63732096, 69222464, 69424640, 70083584, 80778752, 84783104, 85458944, 90256383, 92478000, 116469899, 118063231, 121900544
Offset: 1

Views

Author

Amiram Eldar, Oct 04 2024

Keywords

Examples

			10624 is a term since both 10624 and 10625 are in A376617: 10624/A000120(10624) = 2656, 2656/A000120(2656) = 664, and 664/A000120(664) = 166 are integers, and 10625/A000120(10625) = 2125, 2125/A000120(2125) = 425, and 425/A000120(425) = 85 are integers.

Links

Crossrefs

Subsequence of A330931, A376617 and A376793.
Cf. A000120.

Programs

  • Mathematica
    q[k_] := q[k] = Module[{w = DigitCount[k, 2, 1], w2, m, n}, IntegerQ[m = k/w] && Divisible[m, w2 = DigitCount[m, 2, 1]] && Divisible[n = m/w2, DigitCount[n, 2, 1]]]; Select[Range[1.2*10^6], q[#] && q[#+1] &]
  • PARI
    s(n) = {my(w = hammingweight(n)); if(w == 1, 0, if(n % w, 1, 1 + s(n/w)));}
is1(k) = {my(sk = s(k)); sk == 0 || sk >= 4;}
lista(kmax) = {my(q1 = is1(1), q2); for(k = 2, kmax, q2 = is1(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2);}

A377271 Numbers k such that k and k+1 are both terms in A377209.

Original entry on oeis.org

1, 2, 3, 4, 5, 12, 89, 1824, 3024, 7024, 15084, 17184, 18935, 22624, 28657, 29424, 31464, 37024, 38835, 40032, 42679, 44975, 47375, 66744, 66815, 78219, 89495, 107456, 112175, 119744, 144599, 148519, 169883, 171941, 172025, 188208, 207935, 226624, 244404, 248255
Offset: 1

Views

Author

Amiram Eldar, Oct 22 2024

Keywords

Examples

			1824 is a term since both 1824 and 1825 are in A377209: 1824/A007895(1824) = 304 and 304/A007895(304) = 76 are integers, and 1825/A007895(1825) = 365 and 365/A007895(365) = 73 are integers.

Links

Crossrefs

Cf. A007895, A376793 (binary analog).
Subsequence of A328208, A328209 and A377209.
Subsequences: A377272, A377273.

Programs

  • Mathematica
    zeck[n_] := Length[DeleteCases[NestWhileList[# - Fibonacci[Floor[Log[Sqrt[5]*# + 3/2]/Log[GoldenRatio]]] &, n, # > 1 &], 0]]; (* Alonso del Arte at A007895 *)
q[k_] := q[k] = Module[{z = zeck[k]}, Divisible[k, z] && Divisible[k/z, zeck[k/z]]]; Select[Range[250000], q[#] && q[#+1] &]
  • PARI
    zeck(n) = if(n<4, n>0, my(k=2, s, t); while(fibonacci(k++)<=n, ); while(k && n, t=fibonacci(k); if(t<=n, n-=t; s++); k--); s); \\ Charles R Greathouse IV at A007895
is1(k) = {my(z = zeck(k)); !(k % z) && !((k/z) % zeck(k/z)); }
lista(kmax) = {my(q1 = is1(1), q2); for(k = 2, kmax, q2 = is1(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2); }

A377455 Numbers k such that k and k+1 are both terms in A377385.

Original entry on oeis.org

1, 1224, 126191, 428519, 649727, 1015416, 1988064, 3425856, 4542740, 4574240, 4743900, 4813668, 5131008, 6899840, 7001315, 7172424, 7356096, 8020583, 10206000, 11146421, 11566800, 11597999, 11693807, 12556700, 13742624, 13745759, 13831487, 14365120, 16939799, 20561400
Offset: 1

Views

Author

Amiram Eldar, Oct 29 2024

Keywords

Examples

			1224 is a term since both 1224 and 1225 are in A377385: 1224/A034968(1224) = 204 and 204/A034968(204) = 34 are integers, and 1225/A034968(1225) = 175 and 175/A034968(175) = 35 are integers.

Links

Crossrefs

Cf. A034968.
Subsequence of A118363, A328205 and A377385.
Subsequences: A377456, A377457.
Analogous sequences: A376793 (binary), A377271 (Zeckendorf).

Programs

  • Mathematica
    fdigsum[n_] := Module[{k = n, m = 2, r, s = 0}, While[{k, r} = QuotientRemainder[k, m]; k != 0 || r != 0, s += r; m++]; s]; q[k_] := q[k] = Module[{f = fdigsum[k]}, Divisible[k, f] && Divisible[k/f, fdigsum[k/f]]]; Select[Range[2*10^6], q[#] && q[#+1] &]
  • PARI
    fdigsum(n) = {my(k = n, m = 2, r, s = 0); while([k, r] = divrem(k, m); k != 0 || r != 0, s += r; m++); s;}
is1(k) = {my(f = fdigsum(k)); !(k % f) && !((k/f) % fdigsum(k/f));}
lista(kmax) = {my(q1 = is1(1), q2); for(k = 2, kmax, q2 = is1(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2);}
Showing 1-4 of 4 results.

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

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