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.

A076239 Remainder when 3rd-order composite ccc(n) = A050436(n) is divided by n.

Original entry on oeis.org

0, 1, 1, 2, 3, 3, 1, 6, 3, 2, 4, 1, 11, 10, 10, 8, 6, 6, 7, 8, 6, 4, 3, 2, 2, 0, 26, 0, 0, 28, 28, 29, 28, 27, 28, 28, 30, 29, 28, 30, 29, 31, 31, 30, 29, 29, 28, 28, 27, 26, 28, 29, 29, 30, 30, 29, 31, 30, 29, 32, 31, 30, 29, 28, 29, 28, 27, 26, 26, 25, 26, 26, 26, 26, 26, 28, 29
Offset: 1

Views

Author

Labos Elemer, Oct 08 2002

Keywords

Links

Crossrefs

Cf. A002808, A050435, A050436, A050438, A050439.
Cf. A065860, A076236, A076237, A076238.

Programs

  • Mathematica
    MapIndexed[Mod[#1, First@ #2] &, #] &@ Nest[Values@ KeySelect[ MapIndexed[ First@ #2 -> #1 &, #], CompositeQ] &, Select[Range@ 183, CompositeQ], 2] (* Michael De Vlieger, Jul 22 2017 *)

Formula

a(n) = ccc(n) mod n = A050436(n) mod n.

A064812 Smallest prime p such that the infinite sequence {p, p'=2p-1, p''=2p'-1, ...} begins with a string of exactly n primes.

Original entry on oeis.org

5, 3, 2, 2131, 1531, 33301, 16651, 15514861, 857095381, 205528443121, 1389122693971, 216857744866621, 758083947856951, 107588900851484911, 69257563144280941
Offset: 1

Views

Author

David Terr, Oct 21 2002

Keywords

Comments

Chains of length n of nearly doubled primes.
Smallest prime beginning a complete Cunningham chain of length n of the second kind. (For the first kind see A005602.) - Jonathan Sondow, Oct 30 2015

Examples

			a(3) = 2 because 2 is the smallest prime such that the sequence {2, 3, 5, 9, ...} begins with exactly 3 primes, where each term in the sequence is twice the preceding term minus 1.

Links

Crossrefs

A better version of A005603.
Cf. (A005382 and A005383), A057326, A057327, A057328, A057329, A057330, A005602.
Cf. A002808, A006450, A049076-A049081, A050436, A076237-A076239, A050436-A050439, A065860, A181697, A263879.

A076236 a(n) = A050435(n) mod A002808(n).

Original entry on oeis.org

1, 0, 7, 7, 8, 9, 10, 10, 10, 10, 12, 12, 12, 12, 13, 13, 13, 14, 15, 16, 16, 16, 16, 16, 17, 17, 17, 18, 19, 19, 19, 20, 20, 20, 21, 22, 22, 22, 22, 23, 23, 24, 24, 24, 24, 25, 25, 25, 25, 25, 26, 26, 27, 28, 28, 28, 30, 30, 30, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 32
Offset: 1

Views

Author

Labos Elemer, Oct 08 2002

Keywords

Comments

Original name: Remainder when 2nd order composite, A050435(n), is divided by first order composite, A002808(n). - Michael De Vlieger, Dec 09 2018

Examples

			Let c(n) be the n-th composite number. a(1) = 1 since c(c(1)) mod c(1) = c(4) mod 4 = 9 mod 4 = 1. a(2) = 0 since c(c(2)) mod c(2) = c(6) mod 6 = 12 mod 6 = 0. - _Michael De Vlieger_, Dec 09 2018

Links

Crossrefs

Cf. A002808, A050435-A050439, A065860, A076237-A076239.

Programs

Formula

a(n) = A050435(n) mod A002808(n).

Extensions

Edited by Michael De Vlieger, Dec 09 2018

A076237 a(n) = A050435(n) mod n.

Original entry on oeis.org

0, 0, 0, 0, 3, 3, 3, 1, 8, 8, 10, 9, 8, 8, 8, 7, 6, 6, 7, 8, 7, 6, 5, 4, 5, 4, 3, 4, 5, 4, 3, 4, 3, 2, 2, 2, 2, 1, 0, 0, 40, 0, 0, 43, 43, 44, 44, 45, 45, 45, 47, 48, 49, 50, 50, 50, 53, 53, 53, 55, 55, 55, 55, 55, 56, 56, 56, 56, 56, 56, 57, 58, 59, 59, 60, 62, 63, 63, 64, 65, 65, 65, 67
Offset: 1

Views

Author

Labos Elemer, Oct 08 2002

Keywords

Crossrefs

Cf. A002808, A050435-A050439, A065860, A076236-A076239.

Programs

  • Mathematica
    Module[{cmps=Select[Range[300],CompositeQ],c2},c2=Table[cmps[[cmps[[n]]]],{n,100}];Mod[#[[1]],#[[2]]]&/@Thread[{c2,Range[Length[c2]]}]] (* Harvey P. Dale, May 02 2022 *)

Formula

a(n) = Mod[cc[n], n] = Mod[A050435(n), n]

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

A076238 a(n) = A050436(n) mod A002808(n).

Original entry on oeis.org

0, 3, 1, 8, 8, 9, 8, 8, 7, 6, 8, 7, 6, 4, 5, 4, 3, 4, 4, 4, 3, 2, 2, 2, 1, 0, 0, 0, 43, 43, 44, 45, 45, 45, 47, 48, 50, 50, 50, 53, 53, 55, 55, 55, 55, 56, 56, 56, 56, 56, 58, 59, 60, 62, 63, 63, 65, 65, 65, 68, 68, 68, 68, 68, 69, 69, 69, 69, 70, 70, 72, 72, 73, 74, 74, 76, 78, 78
Offset: 1

Views

Author

Labos Elemer, Oct 08 2002

Keywords

Crossrefs

Cf. A002808, A050435-A050439, A065860, A076236-A076239.

Formula

a(n)=Mod[ccc[n], c[n]]=Mod[A050436(n), A002808[n]]

A073275 Smallest k such that remainder c(k) mod k = n, where c(k) = A002808(k) = k-th composite number or 0 if no such number exists.

Original entry on oeis.org

4, 3, 0, 0, 0, 0, 8, 10, 11, 14, 19, 20, 25, 28, 29, 32, 37, 42, 43, 48, 51, 52, 57, 60, 65, 72, 75, 76, 79, 80, 83, 96, 99, 104, 105, 114, 115, 120, 125, 128, 133, 138, 139, 148, 149, 152, 153, 164, 175, 178, 179, 182, 187, 188, 197, 202, 207, 212, 213, 218, 221
Offset: 1

Views

Author

Labos Elemer, Jul 22 2002

Keywords

Crossrefs

Cf. A002808, A065860.

Programs

  • Mathematica
    c[x_] := FixedPoint[x+PrimePi[ # ]+1&, x]; t=Table[0, 100]; Do[s=Mod[c[n], n]; If[s<=Length[t]&&t[[s]]==0, t[[s]]=n], {n, 1, 10000}]; t

Formula

a(n) = Min{x; A065860(x)=n}.
Showing 1-7 of 7 results.

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