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).

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

Offset: 0

Author

N. J. A. Sloane, Apr 20 2006

Keywords

• nonn

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

Crossrefs

Cf. A064365, A006509, A112877.

Programs

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

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 *)

Python

from sympy import primerange, prime
def aupton(terms):
  alst = [1]
  for n, pn in enumerate(primerange(1, prime(terms)+1), start=1):
    x = alst[-1] - pn
    alst += [x if x > 0 and x not in alst else alst[-1] + pn]
  return alst
print(aupton(61)) # Michael S. Branicky, May 30 2021

Formula

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