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A242252 Start with n-th odd prime, and repeatedly subtract the greatest prime until either 0 or 1 remains.  (The result is the "primes-greedy residue" of the n-th odd prime, which is "primes-greedy summable" if its residue = 0, as at A242255; see Comments.) 8
1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

Suppose that s = (s(1), s(2), ... ) is a sequence of real numbers such that for every real number u, at most finitely many s(i) are < u, and suppose that x > min(s).  We shall apply the greedy algorithm to x, using terms of s.  Specifically, let i(1) be an index i such that s(i) = max{s(j) < x}, and put d(1) = x - s(i(1)).  If d(1) < s(i) for all i, put r = x - s(i(1)).  Otherwise, let i(2) be an index i such that s(i) = max{s(j) < x - s(i(1))}, and put d(2) = x - s(i(1)) - s(i(2)).  If d(2) < s(i) for all i, put r = x - s(i(1)) - s(i(2)).  Otherwise, let i(3) be an index i such that s(i) = max{s(j) < x - s(i(1)) - s(i(2))}, and put d(3) = x - s(i(1)) - s(i(2)) - s(i(3)).  Continue until reaching k such that d(k) < s(i) for every i, and put r = x - s(i(1)) - ... - s(i(k)).  Call r the s-greedy residue of x, and call s(i(1)) + ... + s(i(k)) the s-greedy sum for x.   If r = 0, call x s-greedy summable.  If s(1) = min(s) < s(2), then taking x = s(i) successively for i = 2, 3,... gives a residue r(i) for each i; call (r(i)) the greedy residue sequence for s.  When s is understood from context, the prefix "s-" is omitted.  For A242252, s = (2,3,5,7,11, ... ) = A000040.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..2000

EXAMPLE

n ... n-th odd prime ... a(n)

1 ... 3 ................ 1 = 3 - 2

2 ... 5 ................ 0 = 5 - 3 - 2

3 ... 7 ................ 0 = 7 - 5 - 2

4 ... 11 ............... 1 = 11 - 7 - 3

5 ... 13 ............... 0 = 13 - 11 - 2

34 .. 149 .............. 1 = 149 - 139 - 7 - 2

MATHEMATICA

z = 200;  s = Table[Prime[n], {n, 1, z}]; t = Table[{s[[n]], #, Total[#] == s[[n]]} &[   DeleteCases[-Differences[FoldList[If[#1 - #2 >= 0, #1 - #2, #1] &, s[[n]], Reverse[Select[s, # < s[[n]] &]]]], 0]], {n, z}]; r[n_] := s[[n]] - Total[t[[n]][[2]]]; tr =  Table[r[n], {n, 2, z}]  (* A242252 *)

c = Table[Length[t[[n]][[2]]], {n, 2, z}] (* A242253 *)

f = 1 + Flatten[Position[tr, 0]]  (* A242254 *)

Prime[f]  (* A242255 *)

f1 = Prime[Complement[Range[Max[f]], f]] (* A242256 *)

(* Peter J. C. Moses, May 06 2014 *)

CROSSREFS

Cf. A242253, A242254, A242255, A242256, A241833, A000040.

Sequence in context: A262855 A204171 A267612 * A283265 A181406 A285252

Adjacent sequences:  A242249 A242250 A242251 * A242253 A242254 A242255

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 09 2014

STATUS

approved

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Last modified May 28 04:27 EDT 2017. Contains 287212 sequences.