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 A114577 Dispersion of the composite numbers. 5
 1, 4, 2, 9, 6, 3, 16, 12, 8, 5, 26, 21, 15, 10, 7, 39, 33, 25, 18, 14, 11, 56, 49, 38, 28, 24, 20, 13, 78, 69, 55, 42, 36, 32, 22, 17, 106, 94, 77, 60, 52, 48, 34, 27, 19, 141, 125, 105, 84, 74, 68, 50, 40, 30, 23, 184, 164, 140, 115, 100, 93, 70, 57, 45, 35, 29, 236, 212, 183 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Column 1 consists of 1 and the primes. As a sequence, this is a permutation of the positive integers. As an array, its fractal sequence is A022446 and its transposition sequence is A114578. The dispersion of the primes is given at A114537. REFERENCES Clark Kimberling, Fractal sequences and interspersions, Ars Combinatoria 45 (1997) 157-168. LINKS Ivan Neretin, Table of n, a(n) for n = 1..4950 Clark Kimberling, Interspersions and Dispersions. Clark Kimberling, Interspersions and dispersions, Proceedings of the American Mathematical Society, 117 (1993) 313-321. EXAMPLE Northwest corner: 1   4   9   16  26  39  56   78 2   6   12  21  33  49  69   94 3   8   15  25  38  55  77   105 5   10  18  28  42  60  84   115 7   14  24  36  52  74  100  133 11  20  32  48  68  93  124  162 MATHEMATICA (* Program computes dispersion array T of increasing sequence s[n] and the fractal sequence f of T; here, T = dispersion of the composite numbers, A114577 *) r = 40; r1 = 10; (* r = # rows of T, r1 = # rows to show*); c = 40; c1 = 12; (* c = # cols of T, c1 = # cols to show*); comp = Select[Range[2, 100000], ! PrimeQ[#] &]; s[n_] := s[n] = comp[[n]]; mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]; rows = {NestList[s, 1, c]}; Do[rows = Append[rows, NestList[s, mex[Flatten[rows]], r]], {r}]; t[i_, j_] := rows[[i, j]]; TableForm[Table[t[i, j], {i, 1, r1}, {j, 1, c1}]] (* A114577 array *) u = Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A114577 sequence *) row[i_] := row[i] = Table[t[i, j], {j, 1, c}]; f[n_] := Select[Range[r], MemberQ[row[#], n] &] v = Flatten[Table[f[n], {n, 1, 100}]]  (* A022446, fractal sequence *) (* - Clark Kimberling, Oct 09 2014 *) CROSSREFS Cf. A022446, A114537, A114578. Sequence in context: A082156 A283941 A285090 * A285089 A191426 A182702 Adjacent sequences:  A114574 A114575 A114576 * A114578 A114579 A114580 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Dec 09 2005 STATUS approved

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Last modified January 20 22:57 EST 2020. Contains 331104 sequences. (Running on oeis4.)