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.
Original entry on oeis.org
1, 81, 1296, 2187, 1419857
Offset: 1
Pairs b,c of consecutive
terms of A076467
A378165
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...
A378165 gives the corresponding values of c-b.
-
\\ 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)
A378166
Terms c = A076467(k) such that the distinct prime factors of b = A076467(k-1) and of c-b are subsets of the prime factors of c, i.e., rad(c)/rad((c-b)*b*c) = 1.
Original entry on oeis.org
16, 64, 2744, 474552, 157529610000, 407165596771032, 1491025241529616, 173903694695292024, 661905356066769705912, 14918256451377811247508792, 19801061641727872277815512, 2718924063971620383558231552
Offset: 1
Pairs b,c of consecutive terms of A076467
A378167
c-b b c = a(n)
8, 8, 16,
32, 32, 64,
343, 2401, 2744,
17576, 456976, 474552,
65610000, 157464000000, 157529610000,
11329982936, 407154266788096, 407165596771032,
26102469128, 1490999139060488, 1491025241529616,
315404039943, 173903379291252081, 173903694695292024,
152838610998696, 661905203228158707216, 661905356066769705912.
A378167 gives the corresponding values of c-b.
-
\\ Uses M. F. Hasler's A076467_vec from A076467
rad(x) = vecprod(factor(x)[,1]);
a378166_7(upto) = {my(W=A076467_vec(upto)); for(k=2, #W, my(d=W[k]-W[k-1], q=rad(W[k])/rad(W[k]*W[k-1]*d)); if(q==1, print([d, W[k-1], W[k]])))};
\\ Alternative program not using rad, more efficient
a378166_7(upto) = {my(W=A076467_vec(upto)); for(k=2, #W, my(C=Set(factor(W[k])[,1]), d=W[k]-W[k-1]); if(#setminus(Set(factor(d)[,1]), C)>0, , if(#setminus(Set(factor(W[k-1])[,1]), C)==0, print([d, W[k-1], W[k]]))))};
a378166_7(10^18)
Showing 1-2 of 2 results.
Comments