A353531 Numbers k such that the smallest prime that does not divide them is of the form 4m+3.

2, 4, 8, 10, 14, 16, 20, 22, 26, 28, 30, 32, 34, 38, 40, 44, 46, 50, 52, 56, 58, 60, 62, 64, 68, 70, 74, 76, 80, 82, 86, 88, 90, 92, 94, 98, 100, 104, 106, 110, 112, 116, 118, 120, 122, 124, 128, 130, 134, 136, 140, 142, 146, 148, 150, 152, 154, 158, 160, 164, 166, 170, 172, 176, 178, 180, 182, 184, 188, 190, 194, 196, 200, 202, 206, 208, 210, 212

Offset

1,1

Comments

Numbers k such that A053669(k) is in A002145.

The asymptotic density of this sequence is Sum_{p prime, p == 3 (mod 4)} ((p-1)/(Product_{q prime, q <= p} q)) = 0.3662357207... . - Amiram Eldar, Jul 25 2022

Links

Table of n, a(n) for n=1..78.

Mathematica

f[n_] := Module[{p = 2}, While[Divisible[n, p], p = NextPrime[p]]; p]; Select[Range[200], Mod[f[#], 4] == 3 &] (* Amiram Eldar, Jul 25 2022 *)

Prog

(PARI)
A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669
A353529(n) = (3==(A053669(n)%4));
isA353531(n) = A353529(n);
k=0; n=0; while(k<100, n++; if(isA353531(n), k++; print1(n, ", ")));

Crossrefs

Cf. A353530 for the complement among the even numbers.

Cf. A002144, A053669, A353526, A353529 (characteristic function).

Differs from A342050 for the first time at n=77, where a(77) = 210, the term that is missing from A342050, as A342050(77) = 212.

Sequence in context: A356139 A283967 A232745 * A342050 A189782 A047235

Adjacent sequences: A353528 A353529 A353530 * A353532 A353533 A353534

Keyword

nonn

Author

Antti Karttunen, Apr 25 2022

Status

approved