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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

Table of n, a(n) for n=1..7.

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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Last modified December 16 07:41 EST 2017. Contains 296076 sequences.