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A052349
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Lexicographically earliest sequence of distinct positive integers such that no subsequence sums to a prime.
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15
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1, 8, 24, 25, 86, 1260, 1890, 14136, 197400, 10467660, 1231572090, 682616834970
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OFFSET
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1,2
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COMMENTS
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This set was defined by T. W. A. Baumann in The Prime Puzzles and Problems pages. He and C. Rivera obtained the first 10 members. Chris Nash proved that this sequence is infinite.
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LINKS
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EXAMPLE
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a(4) = 25 as 25+1, 25+8, 25+24, 25+1+8, 25+1+24, 25+8+24 and finally 25+1+8+24 all are composite numbers.
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MATHEMATICA
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a[1]=1; a[n_]:=a[n]=(s=Subsets[Array[a, n-1], n-1]; c=a[n-1]; While[d=1; While[!PrimeQ[Total[s[[d]]]+c]&&d<Length@s, d++]; d!=Length@s||PrimeQ[Total[s[[d]]]+c]||PrimeQ@c, c++]; c); Array[a, 8] (* Giorgos Kalogeropoulos, Nov 19 2021 *)
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PROG
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(Python)
from sympy import isprime
from itertools import islice
def agen(start=1): # generator of terms
alst, k, sums = [start], 1, {0} | {start}
while True:
yield alst[-1]
while any(isprime(k + s) for s in sums): k += 1
alst.append(k)
sums.update([k + s for s in sums])
k += 1
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CROSSREFS
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Cf. A128687 (restricted to odd numbers), A128688 (restricted to even numbers).
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KEYWORD
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hard,more,nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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