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.

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A208548 a(n) = floor((4/3)*(2+prime(n)) - prime(n+1)).

Original entry on oeis.org

2, 1, 2, 1, 4, 3, 6, 5, 4, 10, 7, 11, 14, 13, 12, 14, 20, 17, 21, 24, 21, 25, 24, 24, 31, 34, 33, 36, 35, 26, 41, 40, 46, 39, 50, 47, 49, 53, 52, 54, 60, 53, 64, 63, 66, 57, 61, 73, 76, 75, 74, 80, 73, 80, 82, 84, 90, 87, 91, 94, 87, 86, 101, 104, 103, 94, 107
Offset: 1

Views

Author

Zak Seidov, Feb 28 2012

Keywords

Comments

Conjecture: a(n)>0 for all n (cf. A062234, A207480).

Links

Crossrefs

Cf. A062234, A207480.

Programs

  • Mathematica
    Table[Floor[(4/3)*(2+Prime[n])-Prime[n+1]],{n,100}]
Floor[4/3*(2+#[[1]])-#[[2]]]&/@Partition[Prime[Range[70]],2,1] (* Harvey P. Dale, Apr 13 2016 *)

A258326 a(1) = 3; for n > 1, a(n) = a(n-1) + prime(n+2) - 2*prime(n+1) + 2*prime(n) - prime(n-1).

Original entry on oeis.org

3, 4, 8, 8, 14, 14, 20, 24, 24, 34, 34, 38, 44, 48, 52, 54, 64, 64, 68, 76, 76, 84, 90, 92, 98, 104, 104, 110, 122, 116, 132, 132, 146, 140, 154, 156, 160, 168, 172, 174, 188, 182, 194, 194, 208, 210, 214, 224, 230, 234, 234, 248, 246, 256, 262, 264, 274, 274
Offset: 1

Views

Author

Gionata Neri, May 26 2015

Keywords

Comments

Conjecture: except for a(3)=8 and a(8)=24, this is the same as A073271.

Programs

  • Mathematica
    f[n_] := Block[{a = {3}}, g[x_] := a[[x - 1]] + Prime[x + 2] - 2 Prime[x + 1] + 2 Prime@ x - Prime[x - 1]; Do[AppendTo[a, g@ k], {k, 2, n}]; a]; f@ 60 (* Michael De Vlieger, Jun 02 2015 *)
RecurrenceTable[{a[1]==3,a[n]==a[n-1]+Prime[n+2]-2Prime[n+1]+2Prime[n]-Prime[n-1]},a,{n,60}] (* Harvey P. Dale, Mar 25 2019 *)
  • PARI
    v=[3];n=2;while(n<50,v=concat(v,v[#v]+prime(n+2) - 2*prime(n+1)+2*prime(n)-prime(n-1));n++);v \\ Derek Orr, May 30 2015

Formula

For n>1, a(n) = a(n-1) - A062234(n+1) + A062234(n). - Michel Marcus, May 31 2015

A329485 Odd numbers k such that there are no consecutive prime numbers p, q such that 2*(p - k) = q + k.

Original entry on oeis.org

7, 15, 17, 29, 37, 39, 47, 51, 55, 61, 67, 69, 71, 81, 83, 85, 87, 95, 97, 99, 105, 107, 111, 113, 119, 121, 123, 129, 135, 141, 149, 155, 159, 163, 167, 169, 171, 175, 177, 181, 183, 185, 187, 191, 193, 195, 197, 201, 209, 211, 215, 217, 221, 229, 235, 239, 241, 243, 247, 249
Offset: 1

Views

Author

Dimitris Valianatos, Nov 14 2019

Keywords

Comments

The complementary sequence that include the numbers k which do satisfy 2*(p - k) = q + k is {1, 3, 5, 9, 11, 13, 19, 21, 23, 25, 27, 31, 33, 35, 41, 43, 45, 49, 53, 57, 59, ...}. The number 7 does not satisfy the formula, so is the first term of sequence.
The terms of the sequence are the multiples of 3 not included in A062234 and divided by 3.

Examples

			7 is a term because 2*(p - 7) <> q + 7 for every p, q consecutive prime numbers. See comments.

Crossrefs

Cf. A000040, A062234.

Programs

  • PARI
    v=vector(1000); forstep(k=1,299,2,forprime(n=2,1000,p=nextprime(n+1); if(2*(n-k)==p+k,v[k]=1;break))); forstep(k=1,250,2,if(v[k]==0,print1(k", ")))
Previous Showing 31-33 of 33 results.

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

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