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 1-8 of 8 results.

A135681 a(n)=n if n=1 or if n=prime. Otherwise, n=4 if n is even and n=1 if n is odd.

Original entry on oeis.org

1, 2, 3, 4, 5, 4, 7, 4, 1, 4, 11, 4, 13, 4, 1, 4, 17, 4, 19, 4, 1, 4, 23, 4, 1, 4, 1, 4, 29, 4, 31, 4, 1, 4, 1, 4, 37, 4, 1, 4, 41, 4, 43, 4, 1, 4, 47, 4, 1, 4, 1, 4, 53, 4, 1, 4, 1, 4, 59, 4, 61, 4, 1, 4, 1, 4, 67, 4, 1, 4, 71, 4, 73
Offset: 1

Views

Author

Mohammad K. Azarian, Dec 01 2007

Keywords

Links

Crossrefs

Cf. A135679; A135580; A014681; A014682; A014683; A014684; A014685; A014686; A014687; A014688; A014689; A014690.

Programs

  • Mathematica
    a[n_] := If[PrimeQ[n] || n == 1, n, If[EvenQ[n], 4, 1] ]; Table[a[n], {n,1,25}] (* G. C. Greubel, Oct 26 2016 *)

A082454 a(n) = prime(n) + prime(n-1) - a(n-1) with a(0) = a(1) = 0.

Original entry on oeis.org

0, 0, 5, 3, 9, 9, 15, 15, 21, 21, 31, 29, 39, 39, 45, 45, 55, 57, 63, 65, 73, 71, 81, 81, 91, 95, 103, 101, 109, 107, 115, 125, 133, 135, 141, 147, 153, 155, 165, 165, 175, 177, 183, 189, 195, 195, 201, 209, 225, 225, 231, 231, 241, 239, 253, 255, 265, 267, 273, 275
Offset: 0

Views

Author

Labos Elemer, Apr 25 2003

Keywords

Comments

In fact only one initial value is needed.
If initial values were {a(0)=0, a(1)=1} then we would get A014687.
prime(10) + prime(11) = 29 + 31 = a(10) + a(11) = 31 + 29 (order was reversed!).
If initial values were {a(0)=1, a(1)=2} then (after a(0)=1) we would get A000040, the primes, and would have prime(10) + prime(11) = 29 + 31 = a(10) + a(11) = 29 + 31 (identity).
Initial values {a(0)=1, a(1)=3} would give A014686.

Crossrefs

Cf. A000040, A014686, A014687, A082455.

Programs

  • Mathematica
    g[x_] := Prime[x]+Prime[x-1]-g[x-1] g[0]=0; g[1]=0; Table[g[w], {w, 0, 100}]
Prepend[Table[Prime[n] + 2 (-1)^n, {n, 59}],0] (* George Beck, Jun 03 2022 *)
  • PARI
    lista(nn) = {print1(a=0, ", "); print1(a, ", "); for (n=2, nn, a = prime(n) + prime(n-1) - a; print1(a, ", "););} \\ Michel Marcus, Apr 06 2015

Formula

a(n) = prime(n) + 2*(-1)^n. - George Beck, Jun 03 2022

Extensions

Name corrected by George Beck, Jun 03 2022

A082455 a(n) = prime(n) + prime(n-1) - a(n-1), a(0) = 0, a(1) = 4.

Original entry on oeis.org

0, 4, 1, 7, 5, 13, 11, 19, 17, 25, 27, 33, 35, 43, 41, 49, 51, 61, 59, 69, 69, 75, 77, 85, 87, 99, 99, 105, 105, 111, 111, 129, 129, 139, 137, 151, 149, 159, 161, 169, 171, 181, 179, 193, 191, 199, 197, 213, 221, 229, 227, 235, 237, 243, 249, 259, 261, 271, 269, 279
Offset: 0

Views

Author

Labos Elemer, Apr 25 2003

Keywords

Crossrefs

If initial values are {a[0]=0, a[1]=1} we get A014687.
If initial values are {a[0]=1, a[1]=2} we get the primes, A000040.
Initial values {a[0]=1, a[1]=3} give A014686.
See also A082454.

Programs

  • Mathematica
    g[x_] := Prime[x]+Prime[x-1]-g[x-1] g[0]=0; g[1]=4; Table[g[w], {w, 0, 100}]

Extensions

Definition corrected by Georg Fischer, May 15 2024

A083242 For n >= 3, a(n-3) + a(n-2) + a(n-1) + a(n) = prime(n); a(0) = 0, a(1) = 1, a(2) = 1.

Original entry on oeis.org

0, 1, 1, 3, 2, 5, 3, 7, 4, 9, 9, 9, 10, 13, 11, 13, 16, 19, 13, 19, 20, 21, 19, 23, 26, 29, 23, 25, 30, 31, 27, 39, 34, 37, 29, 49, 36, 43, 35, 53, 42, 49, 37, 63, 44, 53, 39, 75, 56, 57, 41, 79, 62, 59, 51, 85, 68, 65, 53, 91, 72, 67, 63, 105, 76, 69, 67, 119
Offset: 0

Views

Author

Labos Elemer, Apr 24 2003

Keywords

Examples

			a(43) + a(44) + a(45) + a(46) = 63 + 44 + 53 + 39 = 199 = p[46]

Links

Crossrefs

Cf. A001223, A034467, A073737, A014687, A083240.

Programs

  • Maple
    f:= proc(n) option remember; ithprime(n) - procname(n-1) - procname(n-2)-procname(n-3) end proc:
f(0):= 0: f(1):= 1: f(2):= 1:
map(f, [$0..100]); # Robert Israel, Aug 20 2024
  • Mathematica
    f[x_] := Prime[x]-f[x-1]-f[x-2]-f[x-3] {f[0]=0, f[1]=1, f[2]=1}; Table[f[w], {w, 0, 20}]

Formula

From Robert Israel, Aug 20 2024: (Start)
a(4*k) = Sum_{j=1..k} A001223(4*j-1).
a(4*k + 1) = 1 + Sum_{j=1..k} A001223(4*j).
a(4*k + 2) = Sum_{j=0..k} A001223(4*j+1).
a(4*k + 3) = 1 + Sum_{j=0..k} A001223(4*j+2). (End)

A135682 a(n)=n if n=1 or if n=prime. Otherwise, n=4 if n is even and n=7 if n is odd.

Original entry on oeis.org

1, 2, 3, 4, 5, 4, 7, 4, 7, 4, 11, 4, 13, 4, 7, 4, 17, 4, 19, 4, 7, 4, 23, 4, 7, 4, 7, 4, 29, 4, 31, 4, 7, 4, 7, 4, 37, 4, 7, 4, 41, 4, 43, 4, 7, 4, 47, 4, 7, 4, 7, 4, 53, 4, 7, 4, 7, 4, 59, 4, 61, 4, 7, 4, 7, 4, 67, 4, 7, 4, 71, 4, 73
Offset: 1

Views

Author

Mohammad K. Azarian, Dec 01 2007

Keywords

Links

Crossrefs

Cf. A000027; A000040; A135679; A135680; A014681; A014682; A014683; A014684; A014685; A014686; A014687; A014688; A014689; A014690; A135681.

Programs

  • Mathematica
    a[n_] := If[PrimeQ[n] || n == 1, n, If[EvenQ[n], 4, 7] ]; Table[a[n], {n,1,25}] (* G. C. Greubel, Oct 26 2016 *)

A135684 a(n)=11 if n is a prime number. Otherwise, a(n)=n.

Original entry on oeis.org

1, 11, 11, 4, 11, 6, 11, 8, 9, 10, 11, 12, 11, 14, 15, 16, 11, 18, 11, 20, 21, 22, 11, 24, 25, 26, 27, 28, 11, 30, 11, 32, 33, 34, 35, 36, 11, 38, 39, 40, 11, 42, 11, 44, 45, 46, 11, 48, 49, 50, 51, 52, 11, 54, 55, 56, 57, 58, 11
Offset: 1

Views

Author

Mohammad K. Azarian, Dec 01 2007

Keywords

Links

Crossrefs

Cf. A000027; A000040; A135679; A135680; A014681; A014682; A014683; A014684; A014685; A014686; A014687; A014688; A014689; A014690; A135681; A135682; A135683.

Programs

  • Magma
    [IsPrime(n) select 11 else n: n in [1..70]]; // Vincenzo Librandi, Feb 22 2013
  • Mathematica
    Table[If[PrimeQ[n], 11, n], {n, 70}] (* Vincenzo Librandi, Feb 22 2013 *)

A172022 a(n) = prime(n) + (-1)^n.

Original entry on oeis.org

1, 4, 4, 8, 10, 14, 16, 20, 22, 30, 30, 38, 40, 44, 46, 54, 58, 62, 66, 72, 72, 80, 82, 90, 96, 102, 102, 108, 108, 114, 126, 132, 136, 140, 148, 152, 156, 164, 166, 174, 178, 182, 190, 194, 196, 200, 210, 224, 226, 230, 232, 240, 240, 252, 256, 264, 268, 272, 276
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jan 22 2010

Keywords

Comments

1 together with A014687.

Examples

			a(1) = prime(1) + (-1)^1 = 2 - 1 = 1.

Crossrefs

Cf. A000040, A014687.

Programs

Formula

a(n+1) = A014687(n).

Extensions

Entries checked by D. S. McNeil, Dec 01 2010

A082456 a(n) = prime(n) + prime(n-1) - a(n-1), with a(0)=0, a(1)=127, and prime(i) is the i-th prime.

Original entry on oeis.org

0, 127, -122, 130, -118, 136, -112, 142, -106, 148, -96, 156, -88, 166, -82, 172, -72, 184, -64, 192, -54, 198, -46, 208, -36, 222, -24, 228, -18, 234, -12, 252, 6, 262, 14, 274, 26, 282, 38, 292, 48, 304, 56, 316, 68, 322, 74, 336, 98, 352, 104, 358, 114, 366, 126, 382, 138, 394, 146, 402, 156, 408, 168, 432, 186, 438
Offset: 0

Views

Author

Labos Elemer, Apr 25 2003

Keywords

Comments

Initial values {0, 1} give A014687.
Initial values {1, 2} give A000040.
Initial values {1, 3} give A014686.

Crossrefs

Cf. A000040, A014686, A014687, A082454, A082455.

Programs

  • Mathematica
    g[x_] := Prime[x]+Prime[x-1]-g[x-1] g[0]=0; g[1]=127; Table[g[w], {w, 0, 100}]
  • PARI
    a(n) = if (n==0, 0, if (n==1, 127, prime(n) + prime(n-1) - a(n-1))); \\ Michel Marcus, Mar 08 2022

Extensions

Entry revised by N. J. A. Sloane, Dec 22 2005
Showing 1-8 of 8 results.

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

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