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A378164
Smaller of consecutive terms b < c of A076467 such that the quality q=log(rad(c))/log(rad((c-b)*b*c)) of the abc-triple c-b,b,c with gcd(c-b,b,c)=1 sets a new record.
3
1, 81, 1296, 2187, 1419857
OFFSET
1,2
COMMENTS
If it exists, a(6)>5*10^27.
EXAMPLE
Pairs b,c of consecutive
terms of A076467
c-b b c Quality = log(rad(c))/log(rad((c-b)*b*c))
7, 1, 8, 0.262649535...
44, 81, 125, 0.277532712...
35, 1296, 1331, 0.309605475...
10, 2187, 2197, 0.429917243...
23040, 1419857, 1442897, 0.431260235...
PROG
(PARI) \\ Uses M. F. Hasler's A076467_vec from A076467
a378164_5(upto) = {my(W=A076467_vec(upto), qw=0); for(k=2, #W, my(d=W[k]-W[k-1]); if(gcd([d, W[k], W[k-1]])==1, my(C=factor(W[k])[, 1], B=factor(W[k-1])[, 1], A=factor(d)[, 1], P=vecprod(setunion(setunion(Set(B), Set(C)), Set(A))), q=log(vecprod(C))/log(P)); if(q>qw, print([d, W[k-1], W[k], q]); qw=q)))};
a378164_5(10^16)
CROSSREFS
A378165 gives the corresponding values of c-b.
Sequence in context: A231994 A236790 A232876 * A224355 A016768 A224014
KEYWORD
nonn,hard,more
AUTHOR
Hugo Pfoertner, Nov 18 2024
STATUS
approved