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A128201 Union of positive squares and the odd numbers. 6
1, 3, 4, 5, 7, 9, 11, 13, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 36, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 64, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 100, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Range of A128200.

Positive numbers n such that n^((1 + n)/2) is an integer. - Gionata Neri, May 07 2016

LINKS

R. Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = f(n,1,1,2) where f(n,i,m,x) = if i=n then m else if m+1=x^2 then f(n,i+1,m+1,x) else if m+1>x^2 then f(n,i+1,m+1,x+2) else f(n,i+1,m+2,x).

Set R = 2n-round(sqrt(2n)), then a(n) = R+sign(frac(sqrt(R)))*(not(R mod 2)). - Gerald Hillier, Apr 16 2015

MATHEMATICA

f[n_] := Block[{s = Range[n]^2, t}, Union[s, Range[1, Last@ s, 2]] // Sort]; f@ 12 (* Michael De Vlieger, Apr 16 2015 *)

PROG

(PARI) A128201(n)=!(bittest(n=2*n-round(sqrt(2*n)), 0)||issquare(n))+n \\ Based on Hiliers's formula. - M. F. Hasler, Apr 19 2015

(PARI) is_A128201(n)=bittest(n, 0)||issquare(n) \\ M. F. Hasler, Apr 19 2015

CROSSREFS

Partial sums given by A157130. - Gerald Hillier, Feb 25 2009

See A176693 for the union of even numbers and the squares. - M. F. Hasler, Apr 19 2015

Sequence in context: A190941 A284752 A161153 * A233514 A096262 A193339

Adjacent sequences:  A128198 A128199 A128200 * A128202 A128203 A128204

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Mar 04 2007

STATUS

approved

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Last modified February 23 23:56 EST 2018. Contains 299595 sequences. (Running on oeis4.)