A247283 Positions of subrecords in A048673.

5, 7, 9, 15, 18, 27, 36, 54, 72, 108, 144, 216, 288, 432, 576, 864, 1152, 1728, 2304, 3456, 4608, 6912, 9216, 13824, 18432, 27648, 36864, 55296, 73728, 110592, 147456, 221184, 294912, 442368, 589824, 884736, 1179648, 1769472, 2359296, 3538944, 4718592, 7077888

Offset: 1

Author

Antti Karttunen, Sep 11 2014

Keywords

• nonn

Comments

Odd bisection seems to be A116453 (i.e. A005010, 9*2^n from a(3)=9 onward).

After terms 7 and 15, even bisection from a(6)=27 onward seems to be A175806 (27*2^n).

Examples

			The fourth (A246360(4) = 5) and the fifth (A246360(5) = 8) record of A048673 (1, 2, 3, 5, 4, 8, ...) occur at A029744(4) = 4 and A029744(5) = 6 respectively. In range between, the maximum must occur at 5, thus a(4-3) = a(1) = 5. (All the previous records of A048673 are in consecutive positions, 1, 2, 3, 4, thus there are no previous subrecords).
The ninth (A246360(9) = 68) and the tenth (A246360(10) = 122) record of A048673 occur at A029744(9) = 24 and A029744(10) = 32 respectively. For n in range 25 .. 31 the values of A048673 are: 25, 26, 63, 50, 16, 53, 19, of which 63 is the maximum, and because it occurs at n = 27, we have a(9-3) = a(6) = 27.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..60

Crossrefs

A247284 gives the corresponding values.

Cf. A005010 (A116453), A175806, A029744, A048673, A064216, A246360, A245449.

Programs

PARI

\\ Compute A245449, A246360, A247283 and A247284 at the same time:
default(primelimit,(2^31)+(2^30));
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From Michel Marcus
A048673(n) = (A003961(n)+1)/2;
n = 0; i2 = 0; i3 = 0; ir = 0; prevmax = 0; submax = 0; while(n < 2^32, n++; a_n = A048673(n); if((A048673(a_n) == n), i2++; write("b245449.txt", i2, " ", n)); if((a_n > prevmax), if(submax > 0, i3++; write("b247283.txt", i3, " ", submaxpt); write("b247284.txt", i3, " ", submax)); prevmax = a_n; submax = 0; ir++; write("b029744_empirical.txt", ir, " ", n); write("b246360_empirical.txt", ir, " ", a_n), if((a_n > submax), submax = a_n; submaxpt = n)));

Scheme

(definec (A247283 n) (max_pt_in_range A048673 (+ (A029744 (+ n 3)) 1) (- (A029744 (+ n 4)) 1)))
(define (max_pt_in_range intfun lowlim uplim) (let loop ((i (+ 1 lowlim)) (maxnow (intfun lowlim)) (maxpt lowlim)) (cond ((> i uplim) maxpt) (else (let ((v (intfun i))) (if (> v maxnow) (loop (+ 1 i) v i) (loop (+ 1 i) maxnow maxpt)))))))

Formula

a(n) = A064216(A247284(n)).

Conjectures from Chai Wah Wu, Jul 30 2020: (Start)

a(n) = 2*a(n-2) for n > 6.

G.f.: x*(3*x^5 - x^3 + x^2 - 7*x - 5)/(2*x^2 - 1). (End)