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 A256188 In positive integers: replace k*(k+1)/2 with the first k numbers. 9
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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)). LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 EXAMPLE .  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,... MATHEMATICA Table[If[OddQ[Sqrt[8n+1]], Range[(Sqrt[8n+1]-1)/2], n], {n, 50}]//Flatten (* Harvey P. Dale, Jun 01 2019 *) PROG (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 CROSSREFS Cf. A255437, A000217, A014132, A002261, A000537, A004202, A014132, A002061, A255878 (first differences), A255879 (partial sums). Sequence in context: A132320 A076369 A319773 * A072727 A292601 A301364 Adjacent sequences:  A256185 A256186 A256187 * A256189 A256190 A256191 KEYWORD nonn AUTHOR Reinhard Zumkeller, Mar 26 2015 STATUS approved

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Last modified October 15 12:31 EDT 2019. Contains 328026 sequences. (Running on oeis4.)