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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.
8
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
1,3
COMMENTS
P_5(i) = the i-th pentagonal number.
LINKS
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.
FORMULA
a(n) = A045929(n) - n + 1.
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 *)
PROG
(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
KEYWORD
nonn,easy
AUTHOR
Grady Bullington (bullingt(AT)uwosh.edu), Sep 14 2006
EXTENSIONS
Definition corrected by Michel Marcus, Apr 01 2013
STATUS
approved