A208884 -id:A208884 - cp's OEIS frontend

A335817 a(k) is the index of the first occurrence of 2*k-1 in A208884, or 0 if it does not occur.

1, 2, 13, 4, 6, 75, 22975, 11, 15, 10, 1417, 37, 17, 12, 573, 19, 16, 49, 28, 227, 34, 18, 26, 31, 1371, 20, 41, 36, 8181, 339, 38, 30, 40, 207, 43, 70, 1113, 91, 235, 32, 63, 203, 50, 60, 103, 48, 189, 42, 421, 57, 74, 98, 65, 259, 11997, 155, 44, 54, 199, 67

Offset: 1

Giovanni Resta, Jun 25 2020

nonn

It is conjectured that A208884 contains all the odd numbers. If so, a(n) > 0 for every n.

			The first terms of A208884 are 1, 3, 3, 7, 3, so a(2*1-1) = 1, a(2*2-1) = 2, and a(2*4-1) = 4.

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A208884.

b[1]=1; b[n_] := b[n] = #/2^IntegerExponent[#, 2] &@ (n + b[n-1]); A = Transpose@ {b /@ #, #} &@ Range[25000]; A = DeleteDuplicatesBy[ Sort@ A, First]; Last /@ TakeWhile[ A, A[[ (First[#] + 1)/2, 1]] == First@# &]

A331409 a(1)=1; for n>1, a(n) = a(n-1)+n, divided by its largest prime factor.

Original entry on oeis.org

1, 1, 2, 2, 1, 1, 4, 4, 1, 1, 4, 8, 3, 1, 8, 8, 5, 1, 4, 8, 1, 1, 8, 16, 1, 9, 12, 8, 1, 1, 16, 16, 7, 1, 12, 16, 1, 3, 6, 2, 1, 1, 4, 16, 1, 1, 16, 32, 27, 7, 2, 18, 1, 5, 12, 4, 1, 1, 12, 24, 5, 1, 32, 32, 1, 1, 4, 24, 3, 1, 24, 32, 15, 1, 4, 16, 3, 27, 2, 2, 1, 1, 12, 32, 9

Offset: 1

Ali Sada, Jan 16 2020

nonn

			For n=4, a(4) = 2+4 divided by its largest prime factor = 6/3 = 2.

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Cf. A006530 (largest prime factor), A208884.

[n eq 1 select 1 else (Self(n-1)+n) div Max(PrimeDivisors(Self(n-1)+n)): n in [1..85]]; // Marius A. Burtea, Feb 17 2020

f[n_] := n/FactorInteger[n][[-1, 1]]; a[1] = 1; a[n_] := a[n] = f[a[n - 1] + n]; Array[a, 100] (* Amiram Eldar, Jan 16 2020 *)
nxt[{n_,a_}]:={n+1,(a+n+1)/FactorInteger[a+n+1][[-1,1]]}; NestList[nxt,{1,1},90][[All,2]] (* Harvey P. Dale, Nov 12 2022 *)

a(n) = if (n==1, 1, my(x=a(n-1)+n); x/vecmax(factor(x)[,1])); \\ Michel Marcus, Feb 20 2020

cp's OEIS Frontend

A335817 a(k) is the index of the first occurrence of 2*k-1 in A208884, or 0 if it does not occur.

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