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).

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

Author

Gionata Neri, May 26 2015

Keywords

• nonn
• easy

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