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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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.

REFERENCES

H. W. Gould, Gilbreath-Proth type sequence generated from Lucky numbers, unpublished.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = A254967(n,0). - Reinhard Zumkeller, Feb 11 2015

MATHEMATICA

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-Fran├žois Alcover, Sep 22 2021 *)

PROG

(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

CROSSREFS

Cf. A000959, A036262, A054977.

Cf. A254967.

Sequence in context: A318584 A177338 A024158 * A129438 A125096 A037862

Adjacent sequences:  A054975 A054976 A054977 * A054979 A054980 A054981

KEYWORD

nonn,easy,nice

AUTHOR

Henry Gould, May 29 2000

EXTENSIONS

More terms from Naohiro Nomoto, Jun 16 2001

STATUS

approved

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Last modified June 28 05:40 EDT 2022. Contains 354903 sequences. (Running on oeis4.)