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 A282772 Starting from F(n), minimum number, greater than 1, of consecutive Fibonacci numbers whose average is an integer. 1
 4, 2, 3, 12, 2, 13, 3, 2, 6, 5, 2, 12, 4, 2, 3, 12, 2, 24, 3, 2, 6, 24, 2, 12, 4, 2, 3, 12, 2, 5, 3, 2, 6, 13, 2, 12, 4, 2, 3, 5, 2, 24, 3, 2, 5, 24, 2, 12, 4, 2, 3, 12, 2, 24, 3, 2, 6, 24, 2, 5, 4, 2, 3, 12, 2, 24, 3, 2, 6, 5, 2, 12, 4, 2, 3, 12, 2, 24, 3, 2, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Entries are 2, 3, 4, 5, 6, 12, 13 and 24. Periodic with period equal to 420. LINKS Paolo P. Lava, Table of n, a(n) for n = 0..1000 FORMULA a(3*k + 1) = 2; a(12*k + 2) = a(12*k + 6) = 3; a(12*k) = 4; a(30*k + 9) = a(30*k + 29) = a(60*k + 44) = 5; a(60*k + 8) = a(60*k + 20) = a(60*k + 32) = a(60*k + 56) = 6; a(60*k + 3) = a(60*k + 11) = a(60*k + 15) = a(60*k + 23) = a(60*k + 27) = a(60*k + 35) = a(60*k + 47) = a(60*k + 51) = 12; a(420*k + 5) = a(420*k + 33) = a(420*k + 117) = a(420*k + 173) = a(420*k + 201) = a(420*k + 257) = a(420*k + 285) = a(420*k + 341) = 13; a(420*k + x) = 24, with x = 17, 21, 41, 45, 53, 57, 65, 77, 81, 93, 101, 105, 113, 125, 137, 141, 153, 161, 165, 177, 185, 197, 213, 221, 225, 233, 237, 245, 261, 273, 281, 293, 297, 305, 317, 321, 333, 345, 353, 365, 377, 381, 393, 401, 405, 413, 417. EXAMPLE a(0) = 4 because F(0) + F(1) + F(2) + F(3) = 0 + 1 + 1 + 2 = 4 and 4/4 = 1; a(1) = 2 because F(1) + F(2) = 1 + 1 = 2 and 2/2 = 1; a(2) = 3 because F(2) + F(3) + F(4) = 1 + 2 + 3 = 6 and 6/3 = 2; a(3) = 12 because F(3) + F(4) + ... + F(13) + F(14) = 2 + 3 + ... + 233 + 377 = 984 and 984/12 = 82. MAPLE with(combinat): P:=proc(q) local a, k, n; for k from 0 to q do a:=fibonacci(k); for n from 1 to q do a:=a+fibonacci(k+n); if type(a/(n+1), integer) then print(n+1); break; fi; od; od; end: P(10^3); MATHEMATICA Table[k = 1; While[! IntegerQ@ Mean@ Take[#, n ;; n + k], k++]; k + 1, {n, Length@ # - 24}] &@ Fibonacci@ Range[0, 419] (* Michael De Vlieger, Mar 06 2017 *) CROSSREFS Cf. A000045, A101907, A111035, A254141. Sequence in context: A026216 A292411 A069547 * A227041 A341055 A098046 Adjacent sequences: A282769 A282770 A282771 * A282773 A282774 A282775 KEYWORD nonn,easy AUTHOR Paolo P. Lava, Mar 03 2017 STATUS approved

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