A276342 Left inverse of A274647.

0, 1, 4, 2, 203, 2597, 3, 5, 16, 14, 12, 10, 8, 6, 97, 15546, 243575589, 404450, 23, 404448, 7, 9, 11, 13, 15, 17, 56, 54, 52, 50, 631, 629, 902, 137, 135, 192, 84974, 84972, 27, 309411696, 131, 22, 20, 18, 85, 111320883, 127, 125

Offset: 0

Author

Antti Karttunen, Sep 04 2016

Keywords

• sign

Comments

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).

Links

• Hugo van der Sanden, Table of n, a(n) for n = 0..211
• Robert Israel, Hugo van der Sanden, Robert Gerbicz, and Benjamin Chaffin Table of a(n) for n = 0..10000. 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)).

Crossrefs

Cf. A274647, A005132.

Programs

Maple

N = 10^6: # to search A274647(n) for n <= N
A[0]:= 0:B[0]:= 0:
for n from 1 to N do
  for k from 1 do
     r:= A[n-1]-k*n;
     if r > 0 and not assigned(B[r]) then
        break
     fi;
     r:= A[n-1]+k*n;
     if not assigned(B[r]) then
        break
     fi
  od;
  A[n]:= r;
  B[r]:= n;
od:
seq(B[n],n=0..100); # Robert Israel, Sep 04 2016

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.

Formula

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

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

Extensions

More terms and updated a-file from Hugo van der Sanden, Sep 05 2016

Updated a-file from Robert Gerbicz, Sep 09 2016

Updated a-file from Benjamin Chaffin, Sep 29 2016