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

%I A255437 #11 Sep 02 2024 19:31:13
%S A255437 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,
%T A255437 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,
%U A255437 40,41,42,43,44,45,46,47,48,1,3,5,7,9,11,13,50,51
%N A255437 In positive integers: replace k^2 with the first k odd numbers.
%C A255437 a(A005448(n)) = 1;
%C A255437 conjecture: a(A068722(n)) = (2*n+1)^2, i.e. A068722(n) = gives the position of the first occurrence of n-th odd square;
%C A255437 A164514(n) = a(A255527(n)) and a(m) < A164514(n) for m < A255527(n).
%H A255437 Reinhard Zumkeller, <a href="/A255437/b255437.txt">Table of n, a(n) for n = 1..10000</a>
%e A255437 .  A000290 | 1,    4,          9,                      16,         . . .
%e A255437 .  A000027 | _,2,3,___,5,6,7,8,_____,10,11,12,13,14,15,_______,17,18,...
%e A255437 .  A158405 | 1,    1,3,        1,3,5,                  1,3,5,7,
%e A255437 .  --------+-------------------------------------------------------------
%e A255437 .     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 .
%o A255437 (Haskell)
%o A255437 a255437 n = a255437_list !! (n-1)
%o A255437 a255437_list = f 0 [1..] a158405_tabl where
%o A255437    f k xs (zs:zss) = us ++ zs ++ f (k + 2) vs zss
%o A255437                      where (us, v:vs) = splitAt k xs
%Y A255437 Cf. A256188, A000290, A000037, A158405, A016742, A164514, A255527, A005448, A255507 (first differences), A255508 (partial sums).
%K A255437 nonn
%O A255437 1,2
%A A255437 _Reinhard Zumkeller_, Mar 23 2015