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A340573
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a(n) is the smallest lesser twin prime p from A001359 such that the distance to the previous lesser twin prime is 6*n.
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1
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11, 29, 59, 641, 101, 347, 2309, 569, 1931, 521, 1787, 419, 1229, 1871, 3671, 2237, 6551, 1427, 21491, 1607, 12377, 4931, 1019, 23201, 809, 19697, 12539, 2549, 38921, 10709, 37547, 8819, 9239, 34031, 6089, 80447, 15581, 46049, 36341, 14867, 38237, 36779, 87509, 71261, 15137, 40427, 13679, 54917, 41141, 50891
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OFFSET
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1,1
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COMMENTS
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Lesser twin primes (with the exception of prime 3) are congruent to 5 modulo 6, which implies that distances between successive pairs of twin primes are 6*k.
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LINKS
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FORMULA
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EXAMPLE
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a(1)=11 because 11 - 5 = 6*1.
a(2)=41 because 41 - 29 = 6*2.
a(3)=59 because 59 - 41 = 6*3.
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MATHEMATICA
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Table[a[n] = 0, {n, 1, 10000}]; Table[
b[n] = 0, {n, 1, 10000}]; qq = {}; prev = 5; Do[
If[Prime[n + 1] - Prime[n] == 2, k = (Prime[n] - prev)/6;
If[b[k] == 0, a[k] = Prime[n]; b[k] = 1]; prev = Prime[n]], {n, 5,
10000}]; list = Table[a[n], {n, 1, 50}]
(* Second program: *)
pp = Select[Prime[Range[10^4]], PrimeQ[#+2]&];
dd = Differences[pp];
a[n_] := pp[[FirstPosition[dd, 6n][[1]]+1]];
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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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