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A054978 Obtained from sequence of lucky numbers (A000959) by taking iterated absolute value differences of terms and extracting the leading diagonal. 4

%I

%S 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,

%T 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,

%U 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

%N Obtained from sequence of lucky numbers (A000959) by taking iterated absolute value differences of terms and extracting the leading diagonal.

%C 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.

%D H. W. Gould, Gilbreath-Proth type sequence generated from Lucky numbers, unpublished.

%H Reinhard Zumkeller, <a href="/A054978/b054978.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = A254967(n,0). - _Reinhard Zumkeller_, Feb 11 2015

%t nmax = 104; (* index of last term *)

%t imax = 400; (* max index of initial lucky array L *)

%t L = Table[2 i + 1, {i, 0, imax}];

%t For[n = 2, n < Length[L], r = L[[n++]]; L = ReplacePart[L, Table[r*i -> Nothing, {i, 1, Length[L]/r}]]];

%t T[n_, n_] := If[n + 1 <= Length[L], L[[n + 1]], Print["imax should be increased"]; 0];

%t T[n_, k_] := T[n, k] = Abs[T[n, k + 1] - T[n - 1, k]];

%t a[n_] := T[n, 0];

%t Table[a[n], {n, 0, nmax}] (* _Jean-Fran├žois Alcover_, Sep 22 2021 *)

%o (Haskell)

%o a054978 n = a054978_list !! n

%o a054978_list = map head $ iterate

%o (\lds -> map abs $ zipWith (-) (tail lds) lds) a000959_list

%o -- _Reinhard Zumkeller_, Feb 10 2015

%Y Cf. A000959, A036262, A054977.

%Y Cf. A254967.

%K nonn,easy,nice

%O 0,2

%A _Henry Gould_, May 29 2000

%E More terms from _Naohiro Nomoto_, Jun 16 2001

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Last modified August 10 04:27 EDT 2022. Contains 356029 sequences. (Running on oeis4.)