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 A147302 a(n) = such k where records occured in expression Log[k]/Log[A147298(k)] 8
 2, 9, 81, 128, 2401, 4375, 6436343 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(n) = Numbers a(n) such that a(n)/R(m a(n)(a(n)-m)) > a(n-1)/R(g a(n-1)(a(n-1)-g)) 0 < m < a(n) and 0 < g < a(n-1). This sequence is list of successive records in abc conjecture. No more terms up to 10^20. For smallest values of function rad(m n (n - m)) see A147298. For biggest values of function rad(m n (n - m)) see A147299. For numbers m for which rad(m n (n - m)) reached minimal value see A147300. For numbers m for which rad(m n (n - m)) reached maximal value see A147301. LINKS Carlos Rivera, Puzzle 901. A question about consecutive integers, Prime Puzzles. MATHEMATICA logmax = 0; aa = {}; Do[min = 10^100; max = 0; ile = 0; Do[If[GCD[m, n, n - m] == 1, ile = ile + 1; s = m n (n - m); k = FactorInteger[s]; g = 1; Do[g = g k[[p]][[1]], {p, 1, Length[k]}]; If[g > max, max = g; mmax = m]; If[g < min, min = g; mmin = m]], {m, 1, n - 1}]; If[(Log[n]/Log[min]) > logmax, logmax = (Log[n]/Log[min]); AppendTo[aa, n]; Print[{N[logmax], n, mmin, min, mmax, max}]; AppendTo[ff, n]], {n, 2, 2500}]; aa CROSSREFS Cf. A085152, A085153, A147298-A147307; Sequence in context: A279055 A135868 A212271 * A112670 A117581 A123570 Adjacent sequences:  A147299 A147300 A147301 * A147303 A147304 A147305 KEYWORD nonn,more,changed AUTHOR Artur Jasinski, Nov 05 2008 STATUS approved

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