A255527 -id:A255527 - cp's OEIS frontend

A255437 In positive integers: replace k^2 with the first k odd numbers.

1, 2, 3, 1, 3, 5, 6, 7, 8, 1, 3, 5, 10, 11, 12, 13, 14, 15, 1, 3, 5, 7, 17, 18, 19, 20, 21, 22, 23, 24, 1, 3, 5, 7, 9, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 1, 3, 5, 7, 9, 11, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 1, 3, 5, 7, 9, 11, 13, 50, 51

Offset: 1

Reinhard Zumkeller, Mar 23 2015

nonn

a(A005448(n)) = 1;
conjecture: a(A068722(n)) = (2*n+1)^2, i.e. A068722(n) = gives the position of the first occurrence of n-th odd square;
A164514(n) = a(A255527(n)) and a(m) < A164514(n) for m < A255527(n).

			.  A000290 | 1,    4,          9,                      16,         . . .
.  A000027 | _,2,3,___,5,6,7,8,_____,10,11,12,13,14,15,_______,17,18,...
.  A158405 | 1,    1,3,        1,3,5,                  1,3,5,7,
.  --------+-------------------------------------------------------------
.     a(n) | 1,2,3,1,3,5,6,7,8,1,3,5,10,11,12,13,14,15,1,3,5,7,17,18,19 .

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

Cf. A256188, A000290, A000037, A158405, A016742, A164514, A255527, A005448, A255507 (first differences), A255508 (partial sums).

a255437 n = a255437_list !! (n-1)
a255437_list = f 0 [1..] a158405_tabl where
   f k xs (zs:zss) = us ++ zs ++ f (k + 2) vs zss
                     where (us, v:vs) = splitAt k xs

A164514 1 followed by numbers that are not squares.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79

Offset: 1

Jaroslav Krizek, Aug 14 2009

Complement of A000290 for n >= 1.

a(n) = A255437(A255527(n)) and A255437(m) < a(n) for m < A255527(n), i.e. record values in A255437.

Cf. A000037, A255437, A255527.

a164514 n = a164514_list !! (n-1)
a164514_list = 1 : a000037_list
-- Reinhard Zumkeller, Mar 23 2015

is(n)=!issquare(n) || n==1 \\ Charles R Greathouse IV, Sep 01 2015

{1} Union A000037.

a(n) = A000037(n-1) = n-1+floor(1/2 + sqrt(n - 1)) = n-1 + floor( sqrt(n-1 + floor( sqrt(n - 1) ))) for n > 1.

Edited by R. J. Mathar, Aug 21 2009

cp's OEIS Frontend

A255437 In positive integers: replace k^2 with the first k odd numbers.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell