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 A327616 Irregular table read by rows; the first row contains a single 1; for any n > 1, row n+1 corresponds to the ordinal transform of the terms in rows 1..n. 2
 1, 1, 1, 2, 1, 2, 3, 1, 1, 2, 3, 1, 4, 2, 1, 5, 1, 2, 3, 1, 4, 2, 1, 5, 6, 3, 2, 7, 1, 4, 8, 1, 1, 2, 3, 1, 4, 2, 1, 5, 6, 3, 2, 7, 1, 4, 8, 1, 9, 5, 3, 10, 2, 6, 11, 2, 1, 4, 7, 1, 12, 3, 1, 13, 1, 2, 3, 1, 4, 2, 1, 5, 6, 3, 2, 7, 1, 4, 8, 1, 9, 5, 3, 10, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The ordinal transform of a sequence b(n) is the sequence t(n) = number of values in b(1), ..., b(n) which are equal to b(n). LINKS Rémy Sigrist, Table of n, a(n) for n = 1..8192 FORMULA Apparently: - the greatest term in row n is A000045(n), - a(n) = 1 iff n = 1 or n belongs to A060138, - a(A048297(n+1)) = n (and this corresponds to the first occurrence of n), - a(4^k) = A000045(2*k+1) for any k >= 0, - a(2*4^k-1) = A000045(2*k+2) for any k >= 0. EXAMPLE Triangle begins: 1: [1] 2: [1] 3: [1, 2] 4: [1, 2, 3, 1] 5: [1, 2, 3, 1, 4, 2, 1, 5] 6: [1, 2, 3, 1, 4, 2, 1, 5, 6, 3, 2, 7, 1, 4, 8, 1] PROG (PARI) { for (n=1, #a=vector(85), print1 (a[n]=if (n==1, a[n]=1, a[n]=o[a[k++]]++)", "); if (hammingweight(n)==1, k=0; o=vector(vecmax(a[1..n])))) } CROSSREFS Cf. A000045, A011782 (row lengths), A048297, A060138, A107946. Sequence in context: A145726 A322984 A277822 * A181631 A348390 A133674 Adjacent sequences: A327613 A327614 A327615 * A327617 A327618 A327619 KEYWORD nonn,look,tabf AUTHOR Rémy Sigrist, Jul 06 2020 STATUS approved

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Last modified May 22 15:18 EDT 2024. Contains 372758 sequences. (Running on oeis4.)