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 1-3 of 3 results.

A376793 Numbers k such that k and k+1 are both in A376616.

Original entry on oeis.org

1, 1424, 2484, 4304, 4655, 6223, 10624, 13824, 20624, 22784, 29448, 33424, 33984, 36944, 41535, 43263, 45184, 45324, 65744, 66199, 68624, 69632, 70784, 74304, 74627, 99584, 103103, 103424, 105720, 114704, 120680, 139904, 147636, 164224, 166144, 192576, 199968
Offset: 1

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Author

Amiram Eldar, Oct 04 2024

Keywords

Examples

			1424 is a term since both 1424 and 1425 are in A376616: 1424/A000120(1424) = 356 and 356/A000120(356) = 89 are integers, and 1425/A000120(1425) = 285 and 285/A000120(285) = 57 are integers.
		

Crossrefs

Subsequence of A330931 and A376616.
Subsequences: A376794, A376795.
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[20000], q[#] && q[#+1] &]
  • PARI
    is1(k) = {my(w = hammingweight(k)); !(k % w) && !((k/w) % hammingweight(k/w));}
    lista(kmax) = {my(q1 = is1(1), q2); for(k = 2, kmax, q2 = is1(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2);}

A377273 Starts of runs of 3 consecutive integers that are terms in A377209.

Original entry on oeis.org

1, 2, 3, 4, 231700599, 1069467839, 1156703470, 1241186868, 2533742848, 2684864798, 3037193808, 5056780650, 7073145000, 7557047134, 9623855878, 12090760318, 12120887700, 13816479742, 14430478270, 15811947072, 16864260048, 20905152190, 22735441078, 23224253128, 23269229774, 23766221400, 25175490262
Offset: 1

Views

Author

Amiram Eldar, Oct 22 2024

Keywords

Examples

			231700599 is a term since 231700599, 231700600 and 231700601 are all terms in A377209: 231700599/A007895(231700599) = 17823123 and 17823123/A007895(17823123) = 1980347 are integers, 231700600/A007895(231700600) = 23170060 and 23170060/A007895(23170060) = 2317006 are integers, and 231700601/A007895(231700601) = 21063691 and 21063691/A007895(21063691) = 1914881 are integers.
		

Crossrefs

Cf. A007895, A376794 (binary analog).
Subsequence of A328208, A328209, A328210, A377209 and A377271.

Programs

  • 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 = is1(2), q3); for(k = 3, kmax, q3 = is1(k); if(q1 && q2 && q3, print1(k-2, ", ")); q1 = q2; q2 = q3);}

A377456 Starts of runs of 3 consecutive integers that are all terms of A377385.

Original entry on oeis.org

39998374960, 326660221888, 520935101440, 723006782783, 923072388208, 977932351240, 1134397887874, 1351753892944, 1864828904536, 2171452161023
Offset: 1

Views

Author

Amiram Eldar, Oct 29 2024

Keywords

Examples

			39998374960 is a term since 39998374960, 39998374961 and 39998374962 are all in A377385: 39998374960/A034968(39998374960) = 999959374, and 999959374/A034968(999959374) = 32256754 are integers, 39998374961/A034968(39998374961) = 975570121, and 975570121/A034968(975570121) = 33640349 are integers, and 39998374962/A034968(39998374962) = 1025599358, and 1025599358/A034968(1025599358) = 30164687 are integers.
		

Crossrefs

Cf. A034968.
Subsequence of A118363, A328205, A377385 and A377455.
Analogous sequences: A376794 (binary), A377273 (Zeckendorf).

Programs

  • 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 = is1(2), q3); for(k = 3, kmax, q3 = is1(k); if(q1 && q2 && q3, print1(k-2, ", ")); q1 = q2; q2 = q3);}
Showing 1-3 of 3 results.