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A078571 Total number of prime factors of the average of n-th twin prime pair. 7
2, 2, 3, 3, 3, 3, 4, 5, 3, 5, 3, 4, 5, 7, 4, 4, 6, 5, 3, 5, 4, 5, 7, 4, 4, 4, 6, 3, 3, 5, 6, 3, 5, 4, 5, 5, 5, 5, 4, 5, 9, 4, 4, 4, 4, 6, 5, 5, 4, 6, 5, 7, 4, 3, 4, 4, 7, 3, 5, 5, 5, 5, 3, 6, 8, 4, 5, 3, 7, 5, 6, 3, 5, 9, 3, 9, 5, 5, 5, 3, 6, 7, 7, 8, 4, 4, 6, 5, 8, 4, 4, 3, 5, 7, 5, 3, 4, 7, 5, 5, 5, 3, 4, 4, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Between every twin prime pair is a composite number. This sequence looks at a characteristic of those numbers. If the number, n, is the average of a twin prime pair, p&q, then n=(p+q)/2 and p*q=n^2 -1. [Robert G. Wilson v, Aug 02 2010]
LINKS
FORMULA
a(n) = A001222(A014574(n)).
EXAMPLE
12th twin prime pair = (A001359(12), A006512(12)) = (149,151), hence A014574(12) = 150 = 2*3*5*5, therefore a(12) = 4.
From Robert G. Wilson v, Aug 02 2010: (Start)
2) 4, 6 and no others < 10^9.
3) 12, 18, 30, 42, 102, 138, 282, 618, 642, 822, 1698, 1878, 2082, ...
4) 60, 150, 198, 228, 348, 462, 522, 570, 858, 1062, 1230, 1278, ...
5) 72, 108, 180, 270, 312, 420, 660, 828, 882, 1020, 1032, 1050, ...
6) 240, 600, 810, 1320, 1488, 2088, 2340, 2970, 3300, 4158, 4272, ...
7) 192, 432, 1620, 1872, 2268, 3000, 3120, 3528, 3672, 4050, 4128, ...
8) 2112, 3168, 3360, 5280, 7128, 7560, 9000, 12240, 13680, 16632, ...
9) 1152, 2592, 2688, 4800, 7488, 9720, 18048, 29760, 34848, 35280, ...
10) 14592, 21600, 22272, 29568, 32832, 33600, 64152, 71808, 75168, ...
11) 26112, 26880, 49920, 81648, 100800, 102912, 108288, 131712, ...
12) 15360, 23040, 58368, 95232, 133632, 134400, 196992, 219648, ...
13) 139968, 235008, 241920, 279552, 365568, 472392, 617472, 694272, ...
14) 138240, 202752, 345600, 684288, 724992, 783360, 817152, 875520, ...
... (End)
MATHEMATICA
f[n_] := Plus @@ Last /@ FactorInteger@n; p = 3; lst = {}; While[p < 1000, If[ PrimeQ[p + 2], AppendTo[lst, f[p + 1]]]; p = NextPrime@p]: lst (* Robert G. Wilson v, Aug 02 2010 *)
CROSSREFS
Sequence in context: A294242 A241092 A055656 * A362970 A194343 A071860
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Nov 29 2002
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)