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Select[Range[120], CoprimeQ[#, Floor[#/16]]&] (* Harvey P. Dale, Mar 12 2023 *)

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i=n=0; while(i++, if(gcd(i, i\16)==1, a[n++]=i; if(n==#a, break)))))); a

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Stanislav Sykora, <a href="https://oeis.org/wiki/File:VectorUtilities.txt">PARI/GP scripts: Vector utilities</a>

(PARI) a=vector(20000);

i=n=0; while(PARI) RT16Coprimei++, if(n)=gcd(n, ni, i\16)==1; \\ The condition, a[n++]=i; if(n==#a, break)))

v=ListNCond0(20000, RT16Coprime) \\ See the 'Vector utilities' link

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Stanislav Sykora: Further changes as discussed in A248499

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1, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 50, 52, 53, 55, 56, 58, 59, 61, 62, 65, 67, 69, 71, 73, 75, 77, 79, 81, 82, 83, 84, 86, 87, 88, 89, 91, 92, 93, 94, 97, 101, 103, 107, 109, 113, 114, 115, 116, 117, 118, 120, 121, 122, 123, 124, 125, 127, 129, 131, 133, 135, 137

Definition of 'being coprime' and special-case conventions are as in Wikipedia. In particular, when m<16 then Efloor(m/16)=0, and zero is coprime only to 1. The complementary sequence is A248502.

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