|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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))
|
|
FORMULA
|
|
|
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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Grady Bullington (bullingt(AT)uwosh.edu), Sep 14 2006
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|