This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
import Data.List (delete)
a078783 n = a078783_list !! n
(a078783_list, a117073_list) = unzip $
(0,0) : (1,1) : (3,2) : f 3 2 (2:[4..]) where
f a d ms@(m:_) = (a', d') : f a' d' (delete a' ms) where
(a', d') = if i > d then (m, i) else (a + d + 1, d + 1)
i = a - m
-- Reinhard Zumkeller, May 01 2015
a[0] = 0; a[1] = 1;
a[n_] := a[n] = For[m = 2, True, m++, If[FreeQ[Array[a, n-1], m], If[Abs[m - a[n-1]] > Abs[a[n-1] - a[n-2]], Return[m]]]];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Aug 02 2018 *)
To find a(9) we try subtracting the 9th prime, which is 23, from a(8), which is 37. 37 - 23 = 14, but 14 is already in the sequence (it is a(5)), so we must add. a(9) = 37 + 23 = 60.
import Data.Set (singleton, notMember, insert)
a064365 n = a064365_list !! n
a064365_list = 0 : f 0 a000040_list (singleton 0) 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
a = {0}; Do[ If[ a[ [ -1 ] ] - Prime[ n ] > 0 && Position[ a, a[ [ -1 ] ] - Prime[ n ] ] == {}, a = Append[ a, a[ [ -1 ] ] - Prime[ n ] ], a = Append[ a, a[ [ -1 ] ] + Prime[ n ] ] ], {n, 1, 70} ]; a (* Modified by Ivan N. Ianakiev, Aug 05 2019, to accommodate the new initial term of a(0). *)
A064365(N,s/*=1 to print all terms*/)={ my(a=0,u=0); N & forprime(p=1,prime(N), s & print1(a","); u=bitor(u,2^a+=if(a<=p || bittest(u,a-p),p,-p)));a} \\ M. F. Hasler, Mar 07 2012
from sympy import primerange, prime
def aupton(terms):
alst = [0]
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(60)) # Michael S. Branicky, May 30 2021
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