A122798 A P_5-stuttered arithmetic progression with a(n+1) = a(n) if n is a pentagonal number, a(n+1) = a(n)+4 otherwise.

1, 1, 5, 9, 13, 13, 17, 21, 25, 29, 33, 37, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 73, 77, 81, 85, 89, 93, 97, 101, 105, 109, 113, 117, 121, 121, 125, 129, 133, 137, 141, 145, 149, 153, 157, 161, 165, 169, 173, 177, 181, 181, 185, 189, 193, 197, 201, 205, 209

Offset: 1

Author

Grady Bullington (bullingt(AT)uwosh.edu), Sep 14 2006

Keywords

• nonn
• easy

Comments

P_5(i) = the i-th pentagonal number.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Grady D. Bullington, The Connell Sum Sequence, J. Integer Seq. 10 (2007), Article 07.2.6. (includes direct formula for a(n))
• Douglas E. Iannucci and Donna Mills-Taylor, On Generalizing the Connell Sequence, J. Integer Sequences, Vol. 2, 1999, #99.1.7.

Crossrefs

Cf. A001614, A122793, A122794, A122795, A122796, A122797, A122799, A122800.

Programs

Mathematica

nxt[{n_,a_}]:={n+1,If[IntegerQ[(1+Sqrt[24n+25])/6],a,a+4]}; Join[{1}, Transpose[ NestList[nxt,{1,1},60]][[2]]] (* Harvey P. Dale, May 07 2015 *)
nxt[{n_,a_}]:=With[{pn=PolygonalNumber[5,Range[0,30]]},{n+1,If[MemberQ[pn,n],a,a+4]}]; NestList[nxt,{1,1},100][[;;,2]] (* Harvey P. Dale, Sep 28 2023 *)

PARI

lista(m) = {aa = 1; for (i=1, m, print1(aa, ", "); if (! ispolygonal(i, 5), aa += 4););} \\ Michel Marcus, Apr 01 2013, May 02 2015

Formula

a(n) = A045929(n) - n + 1.

Extensions

Definition corrected by Michel Marcus, Apr 01 2013