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

1,1

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

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

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

Adjacent sequences: A062304 A062305 A062306 * A062308 A062309 A062310

Keyword

easy,nonn

Author

Naohiro Nomoto, Mar 28 2002

Status

approved