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A256188 In positive integers: replace k*(k+1)/2 with the first k numbers. 9

%I #21 Jun 04 2022 13:22:18

%S 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,

%T 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,

%U 3,4,5,6,7,8,37,38,39,40,41,42,43,44,1,2,3,4

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

%C a(A002061(n)) = 1;

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

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

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

%H Reinhard Zumkeller, <a href="/A256188/b256188.txt">Table of n, a(n) for n = 1..10000</a>

%e . A000217 | 1, 3, 6, 10, 15, . . .

%e . A000027 | _,2,___,4,5,_____,7,8,9,_______,11,12,13,14,_________,16,...

%e . A002260 | 1, 1,2, 1,2,3, 1,2,3,4, 1,2,3,4,5,

%e . --------+-------------------------------------------------------------

%e . 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,...

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

%o (Haskell)

%o a256188 n = a256188_list !! (n-1)

%o a256188_list = f 0 [1..] a002260_tabl where

%o f k xs (zs:zss) = us ++ zs ++ f (k + 1) vs zss

%o where (us, v:vs) = splitAt k xs

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

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Mar 26 2015

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