A255879 -id:A255879 - cp's OEIS frontend

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

Reinhard Zumkeller, Mar 26 2015

nonn

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)).

			.  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,...

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

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

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

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

A255508 Partial sums of A255437.

Original entry on oeis.org

1, 3, 6, 7, 10, 15, 21, 28, 36, 37, 40, 45, 55, 66, 78, 91, 105, 120, 121, 124, 129, 136, 153, 171, 190, 210, 231, 253, 276, 300, 301, 304, 309, 316, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 631, 634, 639, 646, 655, 666, 703, 741, 780, 820, 861

Offset: 1

Reinhard Zumkeller, Mar 23 2015

nonn

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

Cf. A255437, A255879.

a255508 n = a255508_list !! (n-1)
a255508_list = scanl1 (+) a255437_list

cp's OEIS Frontend

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

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