A274647 A variation on Recamán's sequence (A005132): to get a(n), we first try to subtract n from a(n-1): a(n) = a(n-1)-n if positive and not already in the sequence; if not then we try to add n: a(n) = a(n-1)+n if not already in the sequence; if this fails we try to subtract 2n from a(n-1), or to add 2n to a(n-1), or to subtract 3n, or to add 3n, etc., until one of these produces a positive number not already in the sequence.

0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, 42, 63, 41, 18, 66, 91, 65, 38, 94, 123, 93, 124, 92, 59, 127, 162, 126, 89, 51, 90, 50, 132, 174, 131, 87, 177, 223, 176, 128, 79, 29, 80, 28, 81, 27, 82, 26, 83, 141, 200, 140, 201, 139

Offset: 0

Author

Max Barrentine, Aug 12 2016

Keywords

• nonn
• nice

Comments

Is this a permutation of the natural numbers?

After 5.4*10^11 terms, the smallest number which has not appeared is 212. There are 177 numbers under 10000 which have not appeared. - Benjamin Chaffin, Sep 29 2016

Links

• Antti Karttunen, Table of n, a(n) for n = 0..85000
• Index entries for sequences related to Recamán's sequence

Crossrefs

Cf. A005132, A064389.

Left inverse: A276342 (also right inverse, if this sequence is a permutation of nonnegative integers).

Cf. A276438 (gives k that was used when computing a(n), with sign).

Cf. A274648 (another variant).

Programs

Mathematica

f[s_List] := Block[{a = b = 0, k = 1, l = s[[-1]], n = Length@ s}, While[ If[l > k*n && !MemberQ[s, l - k*n], a = l - k*n]; If[ !MemberQ[s, l + k*n], b = l + k*n; Break[]]; a == b == 0, k++]; Append[s, If[a > 0, a, b]]]; Nest[f, {0}, 70]
(* Robert G. Wilson v, Sep 09 2016 *)

Python

l=[0]
for n in range(1, 101):
    i=1
    while True:
        a=l[n - 1]
        x=a - i*n
        if x>0 and x not in l:
            l.append(x)
            break
        y=a + i*n
        if y>0 and not y in l:
            l.append(y)
            break
        else : i+=1
print(l) # Indranil Ghosh, Jun 03 2017

Formula

A276342(a(n)) = n for all n.