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.

A072630 Values of n where A072629 switches from 01010.. into 0000.. or back.

Original entry on oeis.org

1, 7, 19, 53, 147, 403, 1095, 2979, 8103, 22025, 59873, 162753, 442413, 1202603, 3269017, 8886109, 24154951, 65659969, 178482299, 485165195, 1318815733, 3584912845, 9744803445, 26489122129, 72004899337, 195729609427
Offset: 1

Views

Author

Labos Elemer, Jun 28 2002

Keywords

Crossrefs

See also A004648, A072608, A072609, A072610, A072630.

Programs

  • Mathematica
    m[x_] := Mod[x*Floor[Log[x]//N],2]; Do[s=m[n]+m[n+1]; s1=m[n+1]+m[n+2]; If[ !Equal[s1,s],Print[n]],{n,1,1000000}]

Formula

See program below.
a(n) = A000149(n) or A000149(n)-1 whichever is odd. [From Max Alekseyev, Feb 06 2010]

Extensions

More terms from Max Alekseyev, Feb 06 2010

A072631 Floor( n*log(n) ) mod n.

Original entry on oeis.org

0, 1, 0, 1, 3, 4, 6, 0, 1, 3, 4, 5, 7, 8, 10, 12, 14, 16, 17, 19, 0, 2, 3, 4, 5, 6, 7, 9, 10, 12, 13, 14, 16, 17, 19, 21, 22, 24, 25, 27, 29, 30, 32, 34, 36, 38, 39, 41, 43, 45, 47, 49, 51, 53, 0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 29
Offset: 1

Views

Author

Labos Elemer, Jun 28 2002

Keywords

Comments

Compare with A004648 because prime(n) ~ n * log(n).

Links

Crossrefs

Cf. A004648, A072608, A072609, A072610, A072630.

Programs

A072629 Parity of n*floor(log n).

Original entry on oeis.org

0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Labos Elemer, Jun 28 2002

Keywords

Comments

a(n)=1 for n: 3, 5, 7, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 149, 151, .... - Robert G. Wilson v, Feb 01 2015

Examples

			Parity either alternates or it is steadily 0. Intervals of such kind also change and return: 01010...0000....0101.., etc.

Links

Crossrefs

Cf. A004648, A072608, A072609, A072610, A072630.

Programs

Formula

a(n) = n*floor(log(n)) mod 2.

A072623 Numbers n such that A065863(n) = 1, i.e., prime(n) mod (n - Pi(n)) = 1.

Original entry on oeis.org

4, 5, 6, 11, 19, 25, 34, 36, 75, 82, 87, 90, 94, 237, 604, 609, 614, 1583, 1592, 10466, 10467, 10498, 10504, 10505, 70501, 70511, 180227, 180294, 180358, 180443, 180447, 466078, 8103422, 21058343, 21058649, 143052872, 143052877, 143053068
Offset: 1

Views

Author

Labos Elemer, Jun 26 2002

Keywords

Comments

A004648, A065134 and A065863 behave similarly; they grow relatively slowly and drop suddenly at unexpected values of n. Parity of A004648 behaves most regularly.
Each cluster of entries exceeds the previous cluster by a power of e.

Examples

			For the cluster started at n = 10466 the remainders of A065863(n) are as follows: {9089, 9092, 9117, 9127, 9148, 9159, 1, 1, 9180, 9183, 9182, 9179, 9172, 9169, 9168, 9177, 9176, 9178, 9183, 9192, 43}. It behaves like A004648 or A065134.

Crossrefs

Cf. A065860-A065863, A065133-A065135, A072608-A072610, A004648, A057809.

Programs

  • Mathematica
    Do[ If[ Mod[ Prime[n], n-PrimePi[n]] == 1, Print[n]], {n, 1, 150000000}]
(* Second program: *)
Position[Table[Mod[Prime[n], n - PrimePi[n]], {n, 10^6}], 1] // Flatten (* Michael De Vlieger, Jul 30 2017 *)

Extensions

Edited by Robert G. Wilson v, Jun 27 2002

A072632 Solutions to A072631[n]=0.

Original entry on oeis.org

1, 3, 8, 21, 55, 149, 404, 1097, 2981, 8104, 22027, 59875, 162755, 442414, 1202605, 3269018
Offset: 1

Views

Author

Labos Elemer, Jun 28 2002

Keywords

Comments

Essentially the same as A001671.

Examples

			Compare with A072610 [related to A004648].

Crossrefs

Cf. A004648, A072608, A072609, A072610, A072630, A072631, A072610.

Programs

  • Mathematica
    Do[s=Floor[Mod[Floor[n*Log[n]]//N, n]]; If[s==0, Print[n]], {n, 1, 10000000}]

A099641 Number of solutions to x*frac[p(x)/x]<=Log[n] or A004648(n)<=Log[n].

Original entry on oeis.org

1, 5, 6, 12, 13, 14, 15, 31, 32, 34, 69, 73, 74, 75, 76, 77, 181, 445, 1052, 6455, 6456, 6457, 6459, 6460, 6466, 15928, 16055, 40073, 40078, 40080, 40081, 40082, 40083, 40122, 100362, 100364, 100365, 251707, 251711, 251712, 251717, 251719, 251721
Offset: 1

Views

Author

Labos Elemer, Nov 02 2004

Keywords

Comments

Solutions appear in clusters because of features of diagram visible at A004648. Later clusters are introduced by 6455, 15928, 40073, 100362, 251707, 637235, 4124455, respectively.
Number of solutions in consecutive clusters seem to be as follows: 1,2,4,3,6,1,1,1,6,2,7,3 etc..

Crossrefs

Cf. A004648.
Cf. A023143-A023152, A072610.

Programs

  • Mathematica
    ta={{0}};Do[s=w*fra[Prime[w]/w];If[ !Greater[s, Log[n]], Print[w]; ta=Append[ta, w]], {w, 1, 1000000}];ta=Delete[ta, 1]
Showing 1-6 of 6 results.

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