A369271 The smallest positive number that has not yet appeared that is a multiple of the smallest prime that does not divide n.

2, 3, 4, 6, 8, 5, 10, 9, 12, 15, 14, 20, 16, 18, 22, 21, 24, 25, 26, 27, 28, 30, 32, 35, 34, 33, 36, 39, 38, 7, 40, 42, 44, 45, 46, 50, 48, 51, 52, 54, 56, 55, 58, 57, 60, 63, 62, 65, 64, 66, 68, 69, 70, 75, 72, 78, 74, 81, 76, 49, 80, 84, 82, 87, 86, 85, 88, 90, 92, 93, 94, 95, 96, 99, 98

Offset

1,1

Comments

The sequence is conjectured to be a permutation of the positive integers.

The empty product 1 never appears - Michael De Vlieger, Jan 24 2024

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Formula

a(A002110(k-1)) = the k-th prime.

Example

a(7) = 10 as 2 is the smallest prime that does not divide 7, and 10 = 2*5 is the smallest multiple of 2 that has not yet appeared.

Mathematica

nn = 2^10;
c[_] := False; m[_] := 1;
f[x_] := Block[{q = 2}, While[Divisible[x, q], q = NextPrime[q]]; q];
Do[While[c[Set[k, #*m[#]]], m[#]++] &[f[i]];
  Set[{a[i], c[k]}, {k, True}], {i, nn}];
Array[a, nn] (* Michael De Vlieger, Jan 24 2024 *)

Crossrefs

Cf. A369272, A351495, A053669, A002110.

Sequence in context: A352064 A277905 A257802 * A225850 A038150 A182831

Adjacent sequences: A369268 A369269 A369270 * A369272 A369273 A369274

Keyword

nonn

Author

Scott R. Shannon, Jan 18 2024

Status

approved