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A054978
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Obtained from sequence of lucky numbers (A000959) by taking iterated absolute value differences of terms and extracting the leading diagonal.
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4
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1, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2
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OFFSET
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0,2
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COMMENTS
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The classical Gilbreath-Proth Conjecture is that when iterated absolute differences are formed from the sequence of primes, the leading diagonal is 2,1,1,1,1,1,1,1,1,... (see A036262). This is an analog for the lucky numbers sequence.
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REFERENCES
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H. W. Gould, Gilbreath-Proth type sequence generated from Lucky numbers, unpublished.
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
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FORMULA
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a(n) = A254967(n,0). - Reinhard Zumkeller, Feb 11 2015
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MATHEMATICA
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nmax = 104; (* index of last term *)
imax = 400; (* max index of initial lucky array L *)
L = Table[2 i + 1, {i, 0, imax}];
For[n = 2, n < Length[L], r = L[[n++]]; L = ReplacePart[L, Table[r*i -> Nothing, {i, 1, Length[L]/r}]]];
T[n_, n_] := If[n + 1 <= Length[L], L[[n + 1]], Print["imax should be increased"]; 0];
T[n_, k_] := T[n, k] = Abs[T[n, k + 1] - T[n - 1, k]];
a[n_] := T[n, 0];
Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Sep 22 2021 *)
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PROG
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(Haskell)
a054978 n = a054978_list !! n
a054978_list = map head $ iterate
(\lds -> map abs $ zipWith (-) (tail lds) lds) a000959_list
-- Reinhard Zumkeller, Feb 10 2015
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CROSSREFS
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Cf. A000959, A036262, A054977.
Cf. A254967.
Sequence in context: A318584 A177338 A024158 * A129438 A125096 A037862
Adjacent sequences: A054975 A054976 A054977 * A054979 A054980 A054981
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Henry Gould, May 29 2000
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EXTENSIONS
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More terms from Naohiro Nomoto, Jun 16 2001
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STATUS
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approved
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