A122800 A P_4-stuttered arithmetic progression with a(n+1)=a(n) if n is square, a(n+1)=a(n)+2 otherwise.

1, 1, 3, 5, 5, 7, 9, 11, 13, 13, 15, 17, 19, 21, 23, 25, 25, 27, 29, 31, 33, 35, 37, 39, 41, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 145, 147, 149, 151, 153, 155, 157, 159, 161, 163, 165, 167, 169, 171, 173, 175, 177, 179, 181

Offset: 1

Author

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

Keywords

• nonn
• easy

Comments

P_4(i) = the i-th square.

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, A122798, A122799.

Programs

Mathematica

nxt[{n_,a_}]:={n+1,If[IntegerQ[Sqrt[n+1]],a,a+2]}; NestList[nxt,{0,1},100][[All,2]] (* Harvey P. Dale, Jan 01 2020 *)

PARI

lista(m) = {aa = 1; for (i=1, m, print1(aa, ", "); if (! issquare(i), aa = aa + 2););} \\ Michel Marcus, Apr 01 2013

Formula

a(n) = A045928(n)-n+1.