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Left inverse of A274647.
2

%I #32 Sep 30 2016 13:13:00

%S 0,1,4,2,203,2597,3,5,16,14,12,10,8,6,97,15546,243575589,404450,23,

%T 404448,7,9,11,13,15,17,56,54,52,50,631,629,902,137,135,192,84974,

%U 84972,27,309411696,131,22,20,18,85,111320883,127,125

%N Left inverse of A274647.

%C If A274647 is proved to be a permutation, then this is full inverse of it, and the hypothetical -1's are in that case unnecessary (or can be used as markers for yet unknown values).

%H Hugo van der Sanden, <a href="/A276342/b276342.txt">Table of n, a(n) for n = 0..211</a>

%H Robert Israel, Hugo van der Sanden, Robert Gerbicz, and Benjamin Chaffin <a href="/A276342/a276342_3.txt">Table of a(n) for n = 0..10000</a>. This is based on A274647(n) for n <= 5.4*10^11. The 177 entries of -1 may correspond to values > 5.4*10^11 (first such value is at a(212)).

%F a(n) = index of n in A274647 or -1 if n is not present in that sequence.

%F For all n >= 0, a(A274647(n)) = n.

%p N = 10^6: # to search A274647(n) for n <= N

%p A[0]:= 0:B[0]:= 0:

%p for n from 1 to N do

%p for k from 1 do

%p r:= A[n-1]-k*n;

%p if r > 0 and not assigned(B[r]) then

%p break

%p fi;

%p r:= A[n-1]+k*n;

%p if not assigned(B[r]) then

%p break

%p fi

%p od;

%p A[n]:= r;

%p B[r]:= n;

%p od:

%p seq(B[n],n=0..100); # _Robert Israel_, Sep 04 2016

%o (Scheme) ;; Use the Scheme-code given in A274647. First one needs to compute A274647 up to some high value of n before trying to list terms of this sequence.

%Y Cf. A274647, A005132.

%K sign

%O 0,3

%A _Antti Karttunen_, Sep 04 2016

%E More terms and updated a-file from _Hugo van der Sanden_, Sep 05 2016

%E Updated a-file from _Robert Gerbicz_, Sep 09 2016

%E Updated a-file from _Benjamin Chaffin_, Sep 29 2016