The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A343293 a(n+1) is the smallest preimage k such that A008477(k) = a(n) with a(1) = 36. 2
 36, 64, 81, 512, 196, 16384, 1089, 8589934592, 3844, 4611686018427387904, 31329, 191561942608236107294793378393788647952342390272950272, 478864 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Equivalently, when g is the reciprocal map of f = A008477 as defined in the Name, the terms of this sequence are the successive terms of the infinite iterated sequence {m, g(m), g(g(m)), g(g(g(m))), ...} that begins with m = a(1) = 36, hence f(a(n)) = a(n-1). Why choose 36? Because it is the smallest integer for which there exists such an infinite iterated sequence, with g(36) = 64; then f(36) = 32 with the periodic sequence (32, 25, 32, 25, ...) (see A062307). Explanation: 36 is the first nonsquarefree number in A342973 that is also squareful. The nonsquarefree terms < 36: 12, 18, 20, 24, 28 in A342973 are not squareful (A332785), so they have no preimage by f. When a(n-1) has several preimages by f, as a(n) is the smallest preimage, this sequence is well defined (see examples). All the terms are nonsquarefree but also powerful, hence they are in A001694. a(n) < a(n+2) (last comment in A008477) but a(n) < a(n+1) or a(n) > a(n+1). Prime factorizations from a(1) to a(13): 2^2*3^2, 2^6, 3^4, 2^9, 2^2*7^2, 2^14, 3^2*11^2, 2^33, 2^2*31^2, 2^62, 3^2*59^2, 2^177, 2^4*173^2. It appears that a(2m) = 2^q for some q>1 and a(2m+1) = r^2 for some r>1. a(14) <= 2^692. LINKS Table of n, a(n) for n=1..13. Annales Concours Général, Sujet Concours Général 2012 (in French, problems). Annales Concours Général, Corrigé Concours Général 2012 (in French, solutions). EXAMPLE a(1) = 36; 64 = 2^6 so f(64) = 6^2 = 36, also 192 = 2^6*3^1 and f(192) = 6^2*1^3 = 36 we have f(64) = f(192) = 36; but as 64 < 192, hence g(36) = 64 and a(2) = 64. a(2) = 64 = f(81) = f(256), but as 81 < 256, g(64) = 81 and a(3) = 81. a(4) = 512 = f(196) = f(400), but as 196 < 400, g(512) = 196 and a(5) = 196. CROSSREFS Cf. A001694, A008477, A062307, A332785, A342973. Sequence in context: A044022 A337862 A082295 * A326666 A272190 A060671 Adjacent sequences: A343290 A343291 A343292 * A343294 A343295 A343296 KEYWORD nonn,more AUTHOR Bernard Schott, Apr 11 2021 EXTENSIONS a(10)-a(13) from Bert Dobbelaere, Apr 13 2021 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 13 01:42 EDT 2024. Contains 374259 sequences. (Running on oeis4.)