A072206 Third terms of triple Peano sequence A071988.

2, 4, 15, 42, 176, 299, 697, 988, 1794, 3683, 4526, 7807, 10701, 12384, 16262, 23479, 32568, 36051, 47972, 57226, 62269, 79158, 91964, 113653, 147537, 166751, 176954, 198592, 210043, 234249, 333502, 366276, 419357, 438128, 540423, 562626, 632867

Offset: 1

Author

Robert G. Wilson v, Jul 03 2002

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000125, A006093, A071988.

Programs

Maple

g:= n -> (n^3+5*n+6)/6:
seq(g(ithprime(i)-1),i=1..100); # Robert Israel, Jun 20 2019

Mathematica

seq[n_Integer?Positive] := Module[{fn01 = 1, fn10 = 1, fnout = 1}, Do[{fn10, fn01, fnout} = {fn10 + 1, fn01 + fn10, fn01 + fnout}, {n - 1}]; {fn10, fn01, fnout}]; Ar = Flatten[ Table[ seq[ Prime[n]], {n, 1, 50}]]; a = {}; Do[a = Append[a, Ar[[n]]], {n, 3, 150, 3}]; a

Formula

Numbers, except 2, satisfy a(n) = 1 + k/3 * (4k^2+5), with k in A005097. - Ralf Stephan, Aug 21 2004

a(n) = (n^3+5*n+6)/6, for n+1 prime, so a(n) = A000125(A006093(n)) - Bert Seghers, Jan 01 2012, corrected by Robert Israel, Jun 20 2019