OFFSET
1,2
COMMENTS
Sequence is a permutation of the positive integers and it is its own inverse permutation.
From Antti Karttunen, Nov 05 2016: (Start)
A016945 gives the positions of even terms.
A029744 (without 3) seems to give the positions of records in this sequence (note that it gives the record positions in related A003961 and A048673) which implies that A083658 (without its term 5) would then give the record values.
(End)
LINKS
FORMULA
From Antti Karttunen, Nov 05 2016: (Start)
a(1) = 1; and for n > 1, if n = a(k) for some k = 1 .. n-1, then a(n) = A064989(n), otherwise a(n) = A003961(n). [After the original definition and R. J. Mathar's Maple-code]
a(1) = 1, and for n > 1, if A055396(n) is odd, a(n) = A003961(n), otherwise a(n) = A064989(n). [The above reduces to this.]
a(n) = product{k>=1} prime(k-((-1)^A055396(n)))^e(k) when n = product{k>=1} prime(k)^e(k).
For n > 1, A055396(a(n)) = A055396(n) - (-1)^A055396(n). [Permutation sends the terms on any odd row of A246278 to the next even row just below, and vice versa.]
(End)
MAPLE
A064989 := proc(n) local a, ifs, p ; a := 1 ; ifs := ifactors(n)[2] ; for p in ifs do if op(1, p) > 2 then a := a* prevprime(op(1, p))^op(2, p) ; fi ; od; RETURN(a) ; end: A003961 := proc(n) local a, ifs, p ; a := 1 ; ifs := ifactors(n)[2] ; for p in ifs do a := a* nextprime(op(1, p))^op(2, p) ; od; RETURN(a) ; end: A118306 := proc(nmin) local a, anxt, i, n ; a := [1] ; while nops(a) < nmin do n := nops(a)+1 ; if n in a then anxt := A064989(n) ; else anxt := A003961(n) ; fi ; a := [op(a), anxt] ; od; a ; end: A118306(100) ; # R. J. Mathar, Sep 06 2007
PROG
(PARI)
A118306(n) = { if(1==n, 1, my(f = factor(n)); my(d = (-1)^primepi(f[1, 1])); for(i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-d)); factorback(f)); }; \\ Antti Karttunen, Nov 06 2016
for(n=1, 10001, write("b118306.txt", n, " ", A118306(n)));
(Scheme) (define (A118306 n) (cond ((= 1 n) n) ((odd? (A055396 n)) (A003961 n)) (else (A064989 n)))) ;; Antti Karttunen, Nov 05 2016
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Leroy Quet, May 14 2006
EXTENSIONS
More terms from R. J. Mathar, Sep 06 2007
A small omission in the definition corrected by Antti Karttunen, Nov 05 2016
STATUS
approved