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 A332341 Prime scale sequence (see comments). 3
 -2, -3, 5, -7, -11, -13, 31, -17, -19, -23, 59, -29, -37, -41, 107, -43, -47, -53, -61, -67, 271, -71, -73, -79, 223, -83, -89, -97, 269, -101, -103, -109, 313, -113, -127, -131, -137, -139, 647, -149, -151, -157, 457, -163, -167, -173, 503, -179, -181, -191, -193, -197, 941 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Take a double-pan balance scale and name the pans "negative" and "positive". At each step, the question is: "Is there an unused prime that would balance the scale if added to the positive pan?" If the answer is positive, add that prime to the positive pan. Otherwise, add the smallest unused prime to the negative pan. Is the number of primes in the positive pan infinite? LINKS Michael S. Branicky, Table of n, a(n) for n = 1..10000 EXAMPLE 2 and 3 unbalance the scale (and are negative), but 5 = 2 + 3 balances it (and is positive). MATHEMATICA a[1]=-2; a[n_]:=a[n]=Module[{tab=Table[a[i], {i, 1, n-1}], totalN=Abs[Total[Select[Table[a[i], {i, 1, n-1}], Negative]]], totalP=Total[Select[Table[a[i], {i, 1, n-1}], Positive]], l=NextPrime[Last[Select[Table[a[i], {i, 1, n-1}], Negative]], -1], m=NextPrime[Abs[Last[Select[Table[a[i], {i, 1, n-1}], Negative]]]]}, If[totalN==totalP, If[PrimePi[tab[[-1]]]-PrimePi[Abs[tab[[-2]]]]==1, -NextPrime[tab[[-1]]], If[FreeQ[Abs[tab], m], -m, While[!FreeQ[Abs[tab], m], m=NextPrime[m]]; -m]], If[PrimeQ[totalN-totalP]&&FreeQ[Abs[tab], totalN-totalP], totalN-totalP, If[FreeQ[Abs[tab], Abs[l]], l, While[!FreeQ[Abs[tab], Abs[l]], l=NextPrime[l, -1]]; l]]]]; a/@Range[53] PROG (Python) from itertools import islice from sympy import isprime, nextprime def agen(): # generator of terms used, d, nextp = set(), 0, 2 while True: if d > 0 and d not in used and isprime(d): used.add(d); yield d; d = 0 while nextp in used: nextp = nextprime(nextp) used.add(nextp); yield -nextp; d += nextp print(list(islice(agen(), 53))) # Michael S. Branicky, May 12 2022 CROSSREFS Cf. A000040, A101544, A332787, A332788. Sequence in context: A342566 A067908 A236128 * A262283 A187614 A191077 Adjacent sequences: A332338 A332339 A332340 * A332342 A332343 A332344 KEYWORD sign AUTHOR Ivan N. Ianakiev, Feb 10 2020 STATUS approved

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Last modified October 4 22:25 EDT 2023. Contains 365888 sequences. (Running on oeis4.)