A256188 In positive integers: replace k*(k+1)/2 with the first k numbers.

1, 2, 1, 2, 4, 5, 1, 2, 3, 7, 8, 9, 1, 2, 3, 4, 11, 12, 13, 14, 1, 2, 3, 4, 5, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 22, 23, 24, 25, 26, 27, 1, 2, 3, 4, 5, 6, 7, 29, 30, 31, 32, 33, 34, 35, 1, 2, 3, 4, 5, 6, 7, 8, 37, 38, 39, 40, 41, 42, 43, 44, 1, 2, 3, 4

Offset: 1

Author

Reinhard Zumkeller, Mar 26 2015

Keywords

• nonn

Comments

a(A002061(n)) = 1;

a(A253169(n)) = n and a(m) != n for m < A253169(n);

a(A000537(n)) = A000217(n) and a(m) != A000217(n) for m < A000537(n);

see A004202 and A014132 for record values greater than 1 and where they occur: A014132(n) = a(A004202(n)).

Examples

			.  A000217 | 1,  3,      6,          10,                 15,       . . .
.  A000027 | _,2,___,4,5,_____,7,8,9,_______,11,12,13,14,_________,16,...
.  A002260 | 1,  1,2,    1,2,3,      1,2,3,4,            1,2,3,4,5,
.  --------+-------------------------------------------------------------
.     a(n) | 1,2,1,2,4,5,1,2,3,7,8,9,1,2,3,4,11,12,13,14,1,2,3,4,5,16,17,...
		

Links

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

Crossrefs

Cf. A255437, A000217, A014132, A002260, A000537, A004202, A014132, A002061, A255878 (first differences), A255879 (partial sums).

Programs

Haskell

a256188 n = a256188_list !! (n-1)
a256188_list = f 0 [1..] a002260_tabl where
   f k xs (zs:zss) = us ++ zs ++ f (k + 1) vs zss
                     where (us, v:vs) = splitAt k xs

Mathematica

Table[If[OddQ[Sqrt[8n+1]],Range[(Sqrt[8n+1]-1)/2],n],{n,50}]//Flatten (* Harvey P. Dale, Jun 01 2019 *)