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 A266401 Self-inverse permutation of natural numbers: a(n) = A064989(A263273(A003961(n))). 9
 1, 2, 5, 4, 3, 10, 17, 8, 13, 6, 11, 20, 9, 34, 71, 16, 7, 26, 19, 12, 23, 22, 21, 40, 41, 18, 227, 68, 31, 142, 29, 32, 53, 14, 67, 52, 61, 38, 107, 24, 25, 46, 59, 44, 65, 42, 73, 80, 49, 82, 197, 36, 33, 454, 55, 136, 137, 62, 43, 284, 37, 58, 571, 64, 45, 106, 35, 28, 89, 134, 15, 104, 47 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Shift primes in the prime factorization of n one step towards larger primes (A003961), then apply the bijective base-3 reverse (A263273) to the resulting odd number, which yields another (or same) odd number, then shift primes in the prime factorization of that second odd number one step back towards smaller primes (A064989). LINKS Antti Karttunen, Table of n, a(n) for n = 1..6560 FORMULA a(n) = A064989(A263273(A003961(n))). As a composition of related permutations: a(n) = A064216(A264996(A048673(n))). Other identities. For all n >= 0: A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.] MATHEMATICA f[n_] := Block[{g, h}, g[x_] := x/3^IntegerExponent[x, 3]; h[x_] := x/g@ x; If[n == 0, 0, FromDigits[Reverse@ IntegerDigits[#, 3], 3] &@ g[n] h[n]]]; g[p_?PrimeQ] := g[p] = Prime[PrimePi@ p + 1]; g[1] = 1; g[n_] := g[n] = Times @@ (g[First@ #]^Last@ # &) /@ FactorInteger@ n; h[n_] := Times @@ Power[Which[# == 1, 1, # == 2, 1, True, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger@ n; Table[h@ f@ g@ n, {n, 82}] (* Michael De Vlieger, Jan 04 2016, after Jean-François Alcover at A003961 and A263273 *) PROG (PARI) A030102(n) = { my(r=[n%3]); while(0 if(!n, n, A030102(n/(3^valuation(n, 3))) * (3^valuation(n, 3))); \\ Taking of the quotient probably unnecessary. A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ Using code of Michel Marcus A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)}; A266401 = n -> A064989(A263273(A003961(n))); for(n=1, 6560, write("b266401.txt", n, " ", A266401(n))); (Scheme) (define (A266401 n) (A064989 (A263273 (A003961 n)))) CROSSREFS Cf. A000035, A003961, A064989, A263273. Cf. A265369, A265904, A266190, A266403 (other conjugates or similar sequences derived from A263273). Cf. also A048673, A064216, A264996, A266402, A266407, A266408. Sequence in context: A235200 A267099 A266416 * A083798 A197377 A172483 Adjacent sequences:  A266398 A266399 A266400 * A266402 A266403 A266404 KEYWORD nonn,base AUTHOR Antti Karttunen, Jan 02 2016 STATUS approved

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Last modified July 28 14:19 EDT 2021. Contains 346335 sequences. (Running on oeis4.)