A062307 Numbers n such that n = A008477(A008477(n)) and n is not A008478.

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

Author

Naohiro Nomoto, Mar 28 2002

Keywords

• easy
• nonn

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)

Examples

			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.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..4336

Crossrefs

A114130 is a subsequence.

Programs

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