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A348671
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a(n) is the least prime p such that there are exactly n primes q < p with 2*p+q prime.
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1
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2, 5, 7, 13, 53, 43, 47, 67, 107, 137, 173, 191, 163, 271, 307, 277, 313, 389, 461, 487, 593, 523, 563, 613, 691, 739, 787, 811, 797, 937, 983, 887, 1039, 1069, 997, 1181, 1117, 1249, 1301, 1453, 1303, 1597, 1399, 1483, 1567, 1721, 1871, 1783, 1693, 1697, 1987, 1877, 1847, 2311, 2143, 2309, 2281
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OFFSET
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0,1
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LINKS
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EXAMPLE
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a(3) = 13 because there are 3 primes q < 13 with 2*13+q prime, namely 2*13+3 = 29, 2*13+5 = 31, 2*13+11 = 37, and no prime < 13 has exactly 3 such primes.
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MAPLE
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P:= [seq(ithprime(i), i=1..10000)]:
M:= 100: V:= Array(0..M): count:= 0:
for k from 1 to 10000 while count < M+1 do
v:= nops(select(isprime, {seq(2*P[k]+P[j], j=1..k-1)}));
if v <= M and V[v] = 0 then
count:= count+1; V[v]:= P[k];
fi
od:
convert(V, list);
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MATHEMATICA
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cnt[p_] := Count[Range[2, p - 1], _?(PrimeQ[#] && PrimeQ[2*p + #] &)]; seq[m_] := Module[{s = Table[0, {m}], c = 0, p = 1, i}, While[c < m, p = NextPrime[p]; i = cnt[p] + 1; If[i <= m && s[[i]] == 0, c++; s[[i]] = p]]; s]; seq[50] (* Amiram Eldar, Dec 13 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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