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A226657
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Smallest of the first four consecutive primes that comprise two sets of primes with difference 2*n.
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10
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5, 7, 23, 389, 409, 1511, 5309, 3373, 7351, 37223, 19867, 18593, 142811, 14563, 13933, 763271, 276637, 174491, 363989, 383179, 180907, 687179, 8066923, 913589, 458069, 6358777, 2507093, 5650871, 9182389, 5256071, 10237391, 9955009, 4091393, 24374033
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OFFSET
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1,1
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COMMENTS
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An equivalent definition of this sequence: smallest prime which gives a cluster of primes with the spacing pattern 2*n; x; 2*n, x > 0.
A229021 gives the record values. - Arkadiusz Wesolowski, Sep 11 2013
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LINKS
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Table of n, a(n) for n=1..34.
Index entries for primes, gaps between
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EXAMPLE
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Difference two - primes: 5, 7, 11, 13.
Difference four - primes: 7, 11, 13, 17.
Difference six - primes: 23, 29, 31, 37.
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MATHEMATICA
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lst = {}; Do[a = 3; While[True, b = NextPrime[a]; If[b - a == n && NextPrime[b, 2] - NextPrime[b] == n, AppendTo[lst, a]; Break[]]; a = b], {n, 2, 68, 2}]; lst
Table[SelectFirst[Partition[Prime[Range[16*10^5]], 4, 1], AllTrue[{#[[2]]-#[[1]], #[[4]]- #[[3]]}, EvenQ]&&#[[2]]-#[[1]]==#[[4]]-#[[3]]==2n&], {n, 35}][[All, 1]] (* Harvey P. Dale, Jun 07 2022 *)
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CROSSREFS
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Cf. A000230, A133429, A133430, A229021, A229028, A229030, A229033, A229034.
Sequence in context: A293861 A321462 A121605 * A229021 A173996 A024864
Adjacent sequences: A226654 A226655 A226656 * A226658 A226659 A226660
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KEYWORD
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nonn
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AUTHOR
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Arkadiusz Wesolowski, Jun 14 2013
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STATUS
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approved
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