login
A062307
Numbers n such that n = A008477(A008477(n)) and n is not A008478.
8
8, 9, 25, 32, 49, 121, 125, 128, 169, 200, 243, 288, 289, 343, 361, 392, 500, 529, 675, 841, 864, 961, 968, 972, 1125, 1152, 1323, 1331, 1352, 1369, 1372, 1568, 1681, 1849, 1944, 2000, 2048, 2187, 2197, 2209, 2312, 2809, 2888, 3087, 3200, 3267, 3456, 3481
OFFSET
1,1
COMMENTS
From Bernard Schott, Mar 29 2021: (Start)
If m is a term, then A008477(m) = q is another term and A008477(q) = m.
The first such pairs (m, q) in lexicographic order are (8, 9), (25, 32), (49, 128), (121, 2048), (125, 243), (169, 8192), (200, 288), (289, 131072), ...
If f = A008477, terms k of this sequence are precisely the ones for which the sequence k, f(k), f(f(k)), f(f(f(k))), ... is periodic with period = 2 (see 1st comment in A008477); example for k = 8, this periodic sequence is 8, 9, 8, 9, 8, 9, ...
Prime powers p^r, p, r primes, p <> r are terms. (End)
LINKS
EXAMPLE
8 = 2^3, A008477(8) = 3^2 = 9 and A008477(9) = 2^3 = 8, so 8 and 9 are terms.
200 = 2^3*5^2, A008477(200) = 3^2*2^5 = 288 and A008477(288) = 2^3*5^2 = 200, so 200 and 288 are terms.
PROG
(PARI) f(n) = factorback(factor(n)*[0, 1; 1, 0]); \\ A008477
isok(m) = my(nm = f(m)); (nm != m) && (f(nm) == m); \\ Michel Marcus, Mar 29 2021
CROSSREFS
A114130 is a subsequence.
Sequence in context: A302554 A124438 A124184 * A114130 A130100 A226230
KEYWORD
easy,nonn
AUTHOR
Naohiro Nomoto, Mar 28 2002
STATUS
approved