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Search: a317963 -id:a317963
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Lexicographically earliest infinite sequence of numbers m > 1 with the property that none of the prime indices of m are in the sequence.
+10
64
2, 4, 5, 8, 10, 13, 16, 17, 20, 23, 25, 26, 31, 32, 34, 37, 40, 43, 46, 47, 50, 52, 61, 62, 64, 65, 67, 68, 73, 74, 79, 80, 85, 86, 89, 92, 94, 100, 103, 104, 107, 109, 113, 115, 122, 124, 125, 128, 130, 134, 136, 137, 146, 148, 149, 151, 155, 158, 160, 163
OFFSET
1,1
COMMENTS
A self-describing sequence.
The prime indices of m are the numbers k such that prime(k) divides m.
The sequence is monotonically increasing, since once a number is rejected it stays rejected. Sequence is closed under multiplication for a similar reason. - N. J. A. Sloane, Aug 26 2018
LINKS
EXAMPLE
After the initial term 2, the next term cannot be 3 because 3 has prime index 2, and 2 is already in the sequence. The next term could be 10, which has prime indices 1 and 3, but 4 (with prime index 1) is smaller. So a(2) = 4.
MAPLE
A:= NULL:
P:= {}:
for n from 2 to 1000 do
pn:= numtheory:-factorset(n);
if pn intersect P = {} then
A:= A, n;
P:= P union {ithprime(n)};
fi
od:
A; # Robert Israel, Aug 26 2018
MATHEMATICA
gaQ[n_]:=Or[n==0, And@@Cases[FactorInteger[n], {p_, k_}:>!gaQ[PrimePi[p]]]];
Select[Range[100], gaQ]
CROSSREFS
For first differences see A317963, for primes see A317964.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 16 2018
EXTENSIONS
Added "infinite" to definition. - N. J. A. Sloane, Sep 28 2019
STATUS
approved

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