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

1,1

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).

Links

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

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)

Example

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.

Prog

(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)))))))

Crossrefs

A247284 gives the corresponding values.

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

Sequence in context: A350666 A327307 A029606 * A050595 A182029 A177941

Adjacent sequences: A247280 A247281 A247282 * A247284 A247285 A247286

Keyword

nonn

Author

Antti Karttunen, Sep 11 2014

Status

approved