A274647 -id:A274647 - cp's OEIS frontend

A276438 a(n) = (A274647(n)-A274647(n-1)) / n.

1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 2, 1, -1, -1, 2, 1, -1, 1, -1, -1, 2, 1, -1, -1, -1, 1, -1, 2, 1, -1, -1, 2, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 2, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 2, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1

Offset: 1

Antti Karttunen, Sep 04 2016

sign

a(n) tells what k was finally used when determining the value of A274647(n), with minus sign if subtraction was chosen and with positive sign if addition was chosen.
First 1 occurs at n=1, first 2 at n=24, first 3 at n=128, first 4 at n=204, first 5 at n=17903, first 6 at n=210027.
First -1 occurs at n=4, first -2 at n=124, first -3 at n=5882.

Antti Karttunen, Table of n, a(n) for n = 1..17903

Cf. A274647.

Cf. A276439 (partial sums).

(define (A276438 n) (/ (- (A274647 n) (A274647 (- n 1))) n))

a(n) = (A274647(n)-A274647(n-1)) / n.

A276342 Left inverse of A274647.

Original entry on oeis.org

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

Antti Karttunen, Sep 04 2016

sign

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).

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)).

Cf. A274647, A005132.

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

;; 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.

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.

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

A274648 A variation on Recamán's sequence (A005132): a(n) is the first positive number of the form a(n-1)-nk, k>0 not already in the sequence; and if no such number exists, then a(n) is the first number of the form a(n-1)+nk, k>0 not already in the sequence.

Original entry on oeis.org

0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 5, 45, 66, 44, 67, 19, 69, 17, 71, 15, 73, 103, 72, 40, 106, 38, 108, 36, 110, 34, 112, 32, 114, 30, 116, 28, 118, 26, 120, 168, 119, 169, 16, 68, 121, 175, 65, 177, 63, 179, 61, 181, 59, 183

Offset: 0

Max Barrentine, Aug 12 2016

nonn

Is this a permutation of the natural numbers?
The inverse is: 0, 1, 4, 2, 164, 19, 3, 5, 16, 14, 12, 10, 8, 6, 8228, 28, 51, 26, 158, 24, 7, 9, 11, 13, 15, 17, 46, 90, ..., . Robert G. Wilson v, Sep 07 2016
After 3.2*10^11 terms, the smallest number which has not appeared is 154. - Benjamin Chaffin, Oct 05 2016

Robert G. Wilson v, Table of n, a(n) for n = 0..10000
Index entries for sequences related to Recamán's sequence

Cf. A273148 (inverse), A005132, A274647 (another variant).

f[s_List] := Block[{k = 1, l = s[[-1]], n = Length@ s}, While[ MemberQ[s, l - k*n] && l > k*n, k++]; If[l > k*n, Append[s, l - k*n], k = 1; While[ MemberQ[s, l + k*n], k++]; Append[s, l + k*n]]]; Nest[f, {0}, 60] (* Robert G. Wilson v, Sep 07 2016 *)

A276439 Partial sums of A276438.

Original entry on oeis.org

0, 1, 2, 3, 2, 3, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 6, 7, 6, 7, 6, 5, 7, 8, 7, 6, 8, 9, 8, 9, 8, 7, 9, 10, 9, 8, 7, 8, 7, 9, 10, 9, 8, 10, 11, 10, 9, 8, 7, 8, 7, 8, 7, 8, 7, 8, 9, 10, 9, 10, 9, 8, 10, 11, 10, 9, 8, 9, 8, 9, 10, 11, 10, 9, 8, 9, 8, 10, 11, 10, 11, 10, 9, 8, 9, 10, 11, 10, 11, 12, 13, 12, 11, 10, 9, 8, 9, 10

Offset: 0

Antti Karttunen, Sep 04 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 0..10000

Cf. A274647, A276438
Cf. also A064289, A078759.
Differs from A078759 for the first time at n=24, where a(24)=7 while A078759(24)=6.

a(0) = 0; for n >= 1, a(n) = A276438(n) + a(n-1).

cp's OEIS Frontend

A276438 a(n) = (A274647(n)-A274647(n-1)) / n.

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A276342 Left inverse of A274647.

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Maple

Scheme

Formula

Extensions

A274648 A variation on Recamán's sequence (A005132): a(n) is the first positive number of the form a(n-1)-nk, k>0 not already in the sequence; and if no such number exists, then a(n) is the first number of the form a(n-1)+nk, k>0 not already in the sequence.

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Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A276439 Partial sums of A276438.

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Author

Keywords

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Formula

cp's OEIS Frontend

A276438 a(n) = (A274647(n)-A274647(n-1)) / n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Scheme

Formula

A276342 Left inverse of A274647.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Scheme

Formula

Extensions

A274648 A variation on Recamán's sequence (A005132): a(n) is the first positive number of the form a(n-1)-n*k, k>0 not already in the sequence; and if no such number exists, then a(n) is the first number of the form a(n-1)+n*k, k>0 not already in the sequence.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A276439 Partial sums of A276438.

Views

Author

Keywords

Links

Crossrefs

Formula

A274648 A variation on Recamán's sequence (A005132): a(n) is the first positive number of the form a(n-1)-nk, k>0 not already in the sequence; and if no such number exists, then a(n) is the first number of the form a(n-1)+nk, k>0 not already in the sequence.