A064569 -id:A064569 - cp's OEIS frontend

A333548 Numbers k such that A005132(k-1) = k.

3, 11, 39, 248, 844, 2752, 57071, 58056875

Offset: 1

N. J. A. Sloane, May 01 2020

Subtracting 1 from k gives the index of a term A005132(k-1) = k in Recamán's sequence A005132 such that subtracting k would reach 0. This is not permitted, so we must add k instead, obtaining A005132(k) = 2*k.

If A005132(k-1) = k, A005132(k) = 2*k. The converse is not always true. For example, A005132(75) = 228 and A005132(76) = 228 - 76 = 152. - Seiichi Manyama, May 02 2020

			A005132(10)=11, so 11 is a term (and A005132(11)=22).

Index entries for sequences related to Recamán's sequence

Cf. A005132, A064568, A064569, A187921, A187922, A331659.

A333548_list, A005132_set, y = [], {0}, 0
for n in range(1,10**10):
    y -= n
    if y <= 0 or y in A005132_set:
        y += 2*n
    A005132_set.add(y)
    if y == n+1:
        A333548_list.append(y) # Chai Wah Wu, May 02 2020

a(8) from Chai Wah Wu, May 02 2020

A064568 n-th term in Recamán's sequence A005132 is divisible by n.

Original entry on oeis.org

1, 3, 11, 21, 39, 76, 248, 844, 1520, 2752, 9317, 17223, 31221, 57071, 99741, 589932, 58056875, 101769229, 302890748, 511561220, 904036924, 39488697700, 325374626148, 535755688021, 1404720439053, 3883018238329, 6283167591179, 16166305650060, 25735985498861, 40806937801472

Offset: 1

N. J. A. Sloane, Oct 16 2001

No more terms < 4.61*10^11. - Jud McCranie, Dec 29 2019

No more terms < 6.46*10^13. - James Ewens, Sep 27 2024

			A005132(21) = 63, 63 is divisible by 21, so 21 is in the sequence.

Index entries for sequences related to Recamán's sequence

Cf. A005132, A064569.

With[{s = Nest[Append[#1, If[And[#3 > 0, FreeQ[#1, #3]], #3, #1[[-1]] + #2]] & @@ {#1, #2, #1[[-1]] - #2} & @@ {#, Length@ #} &, {0}, 10^5]}, Reap[Do[If[Mod[s[[i]], i] == 0, Sow[i]], {i, Length@ s - 1}]][[-1, -1]]] (* Michael De Vlieger, Dec 29 2019 *)

Offset changed, a(1), a(22)-a(23) from Jud McCranie, Dec 29 2019

a(24)-a(30) from James Ewens, Sep 27 2024

cp's OEIS Frontend

A333548 Numbers k such that A005132(k-1) = k.

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