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 A332788 Positive-pan primes (see Comments). 3
 5, 31, 59, 107, 271, 223, 269, 313, 647, 457, 503, 941, 1579, 12919, 3571, 1667, 2897, 3037, 3187, 1993, 3461, 2179, 10141, 5927, 11969, 4957, 13627, 5519, 22787, 3851, 3889, 3929, 15217, 44221, 65867, 21799, 10211, 31727, 24623, 11467, 6983, 7039, 16651, 73351 (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 yes, 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 (P) infinite? If it is, is fractalization of P, i.e., further subdivision into PN and PP subpans, possible (including infinitely)? LINKS Michael S. Branicky, Table of n, a(n) for n = 1..10000 EXAMPLE 2 and 3 unbalance the scale (and go to the negative pan N), but 5 = 2 + 3 balances it (and goes to the positive pan P). 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] ]]]; Select[a/@Range[370], Positive] 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); d += nextp print(list(islice(agen(), 44))) # Michael S. Branicky, May 12 2022 CROSSREFS Cf. A075326, A332341, A332787. Sequence in context: A245523 A147033 A125743 * A333243 A078686 A031908 Adjacent sequences: A332785 A332786 A332787 * A332789 A332790 A332791 KEYWORD nonn AUTHOR Ivan N. Ianakiev, Feb 24 2020 EXTENSIONS a(41) and beyond from Michael S. Branicky, May 12 2022 STATUS approved

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Last modified June 4 02:25 EDT 2023. Contains 363118 sequences. (Running on oeis4.)