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A117128 Recamán transform of primes (another version): a(0)=1; for n>0, a(n) = a(n-1) - prime(n) if that number is positive and not already in the sequence, otherwise a(n) = a(n-1) + prime(n). 5
1, 3, 6, 11, 4, 15, 2, 19, 38, 61, 32, 63, 26, 67, 24, 71, 18, 77, 16, 83, 12, 85, 164, 81, 170, 73, 174, 277, 384, 275, 162, 35, 166, 29, 168, 317, 468, 311, 148, 315, 142, 321, 140, 331, 138, 335, 136, 347, 124, 351, 122, 355, 116, 357, 106, 363, 100, 369, 98, 375, 94, 377 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Differs from Cald's sequence A006509 for first time at n=116 (or 117, depending on offset).

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for sequences related to Recamán's sequence

FORMULA

a(n) = A064365(n) + 1. - Thomas Ordowski, Dec 05 2016

MAPLE

M1:=500000; a:=array(0..M1); have:=array(1..M1); a[0]:=1; for n from 1 to M1 do have[n]:=0; od: have[1]:=1;

M2:=2000; nmax:=M2;

for n from 1 to M2 do p:=ithprime(n); i:=a[n-1]-p; j:=a[n-1]+p;

if i >= 1 and have[i]=0 then a[n]:=i; have[i]:=1;

elif j <= M1 then a[n]:=j; have[j]:=1;

else nmax:=n-1; break; fi; od: [seq(a[n], n=0..M2)];

MATHEMATICA

a = {1}; Do[If[And[#1 > 0, ! MemberQ[a, #1]], AppendTo[a, #1], AppendTo[a, #2]] & @@ {#1 - #2, #1 + #2} & @@ {a[[n - 1]], Prime[n - 1]}, {n, 2, 62}]; a (* Michael De Vlieger, Dec 05 2016 *)

PROG

(Haskell)

import Data.Set (singleton, notMember, insert)

a117128 n = a117128_list !! n

a117128_list = 1 : f 1 a000040_list (singleton 1) where

   f x (p:ps) s | x' > 0 && x' `notMember` s = x' : f x' ps (insert x' s)

                | otherwise                  = xp : f xp ps (insert xp s)

                where x' = x - p; xp = x + p

-- Reinhard Zumkeller, Apr 26 2012

CROSSREFS

Cf. A064365, A006509, A112877.

Sequence in context: A304086 A293666 A093903 * A006509 A258928 A144562

Adjacent sequences:  A117125 A117126 A117127 * A117129 A117130 A117131

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 20 2006

STATUS

approved

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Last modified March 21 10:00 EDT 2019. Contains 321368 sequences. (Running on oeis4.)