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A369271
The smallest positive number that has not yet appeared that is a multiple of the smallest prime that does not divide n.
2
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
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
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Jan 18 2024
STATUS
approved