cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A353530 Numbers k such that the smallest prime that does not divide them is of the form 4m+1.

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%I A353530 #12 Jul 25 2022 15:52:25
%S A353530 6,12,18,24,36,42,48,54,66,72,78,84,96,102,108,114,126,132,138,144,
%T A353530 156,162,168,174,186,192,198,204,216,222,228,234,246,252,258,264,276,
%U A353530 282,288,294,306,312,318,324,336,342,348,354,366,372,378,384,396,402,408,414,426,432,438,444,456,462,468,474,486,492
%N A353530 Numbers k such that the smallest prime that does not divide them is of the form 4m+1.
%C A353530 Numbers k such that A053669(k) is in A002144.
%C A353530 The asymptotic density of this sequence is Sum_{p prime, p == 1 (mod 4)} ((p-1)/(Product_{q prime, q <= p} q)) = 0.1337642792... . - _Amiram Eldar_, Jul 25 2022
%e A353530 The smallest prime that does not divide 6 = 2*3, is 5, which is of the form 4m+1, therefore 6 is included in this sequence.
%t A353530 f[n_] := Module[{p = 2}, While[Divisible[n, p], p = NextPrime[p]]; p]; Select[Range[500], Mod[f[#], 4] == 1 &] (* _Amiram Eldar_, Jul 25 2022 *)
%o A353530 (PARI)
%o A353530 A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669
%o A353530 A353528(n) = (1==(A053669(n)%4));
%o A353530 isA353530(n) = A353528(n);
%Y A353530 This is not equal to A342051 \ A005408.
%Y A353530 Cf. A353531 for a complement among the even numbers.
%Y A353530 Cf. A002144, A053669, A353526, A353528 (characteristic function).
%K A353530 nonn
%O A353530 1,1
%A A353530 _Antti Karttunen_, Apr 24 2022