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Search: id:A052187
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| A052187 |
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Primes p such that p, p+d and p+2d are consecutive primes for some d>0. |
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1
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| 3, 47, 199, 20183, 16763, 69593, 255767, 247099, 3565931, 6314393, 4911251, 12012677, 23346737, 43607351, 34346203, 36598517, 51041957, 460475467, 652576321, 742585183, 530324329, 807620651
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OFFSET
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1,1
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COMMENT
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The first term 3 is anomalous since for all others d is divisible by 6. These are minimal terms if in A047948 d=6 is replaced by possible differences: (2), 6, 12, 18, ..., 54, 60.
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FORMULA
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The least p[k ] such that p[k+1 ]=(p[k ]+p[k+2 ])/2 and p[k+1 ]-p[k ]=d is either 2 or divisible by 6.
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EXAMPLE
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a(2)=47 and it is the lower border of a dd pattern: 47[6 ]53[6 ]59. a(10)=6314393 and a(10)+54=6314447, a(10)+108=6314501 are consecutive primes and 6314393 is the smallest prime prior to a (54,54) difference pattern of A001223.
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MATHEMATICA
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a = Table[0, {100}]; NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = q = r = 0; Do[r = NextPrim[r]; If[r + p == 2q && r - q < 201 && a[[(r - q)/2]] == 0, a[[(r - q)/2]] = p; p = q; q = r, {n, 1, 10^8}]; a
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CROSSREFS
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Cf. A001223, A047948, A052160.
Cf. A052188-A052189, A052195-A052198.
Sequence in context: A122535 A058427 A142293 this_sequence A084295 A131465 A137611
Adjacent sequences: A052184 A052185 A052186 this_sequence A052188 A052189 A052190
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jan 28 2000
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EXTENSIONS
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More terms from Labos E. (labos(AT)ana.sote.hu), Jan 04 2002
More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jan 06 2002
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