A147302 Numbers k where records occur in the expression log(k) / log(A147298(k)).

2, 9, 81, 128, 2401, 4375, 6436343

Offset: 1

Author

Artur Jasinski, Nov 05 2008

Keywords

• nonn
• more

Comments

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 the 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)) reaches a minimal value see A147300.

For numbers m for which rad(m*n*(n-m)) reaches a maximal value see A147301.

Links

• Carlos Rivera, Puzzle 901. A question about consecutive integers, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A085152, A085153, A147298-A147307.

Programs

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