A036467 a(n) + a(n-1) = n-th prime.

1, 1, 2, 3, 4, 7, 6, 11, 8, 15, 14, 17, 20, 21, 22, 25, 28, 31, 30, 37, 34, 39, 40, 43, 46, 51, 50, 53, 54, 55, 58, 69, 62, 75, 64, 85, 66, 91, 72, 95, 78, 101, 80, 111, 82, 115, 84, 127, 96, 131, 98, 135, 104, 137, 114, 143, 120, 149, 122, 155, 126, 157, 136, 171, 140, 173

Offset: 0

Author

Maghraoui Abdelkader

Keywords

• nonn
• easy
• nice

Comments

After the initial 1,1, this sequence contains no duplicate values: terms thereafter have opposite parity, and a(n+2) > a(n). Do even and odd values trade the lead infinitely often? (We would expect them to if we model their difference as a random walk.) - Franklin T. Adams-Watters, Jan 25 2010

Links

• T. D. Noe, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A001223, A008347.

Programs

Haskell

a036467 n = a036467_list !! n
a036467_list = 1 : zipWith (-) a000040_list a036467_list
-- Reinhard Zumkeller, Nov 02 2011

Magma

[n lt 2 select 1 else NthPrime(n)-NthPrime(n-1)+Self(n-1): n in [0..65]];  // Bruno Berselli, Jun 18 2011

Mathematica

a[n_] := Abs[1+Sum[(-1)^(k+1)*Prime[k], {k, 2, n}]]; a /@ Range[0, 65] (* Jean-François Alcover, Apr 22 2011 *)
t={1,1};Do[AppendTo[t,NextPrime[t[[-2]]+t[[-1]]]-t[[-1]]],{n,64}];t (* Vladimir Joseph Stephan Orlovsky, Jan 26 2012 *)
Transpose[NestList[{First[#]+1,Prime[First[#]+1]-Last[#]}&,{0,1},70]][[2]] (* Harvey P. Dale, Sep 14 2012 *)

PARI

print1(t=1);forprime(p=2,1e3,print1(", ",t=p-t)) \\ Charles R Greathouse IV, Jun 18 2011

Extensions

More terms from Jud McCranie