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.

A094387 Numbers k such that gcd(k, A000120(k)) = 1.

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%I A094387 #25 Mar 10 2022 04:40:44
%S A094387 1,2,3,4,5,7,8,9,11,13,14,15,16,17,19,22,23,25,26,27,28,29,31,32,33,
%T A094387 35,37,38,39,41,43,44,45,47,49,50,51,52,53,56,57,59,61,62,64,65,67,70,
%U A094387 71,73,74,75,76,77,79,82,83,85,87,88,89,91,93,94,95,97,98,99,100,101,103
%N A094387 Numbers k such that gcd(k, A000120(k)) = 1.
%C A094387 This sequence has density 6/Pi^2 (Olivier, 1975).
%C A094387 All primes, powers of 2, and powers of two plus one are terms of this sequence. - _William Boyles_, Jan 27 2022
%D A094387 Jean-Paul Allouche and Jeffrey Shallit, Automatic Sequences, Cambridge University Press, 2003, p. 117.
%H A094387 Amiram Eldar, <a href="/A094387/b094387.txt">Table of n, a(n) for n = 1..10000</a>
%H A094387 Christian Mauduit, Carl Pomerance and András Sárközy, <a href="https://doi.org/10.1007/s11139-005-0824-6">On the distribution in residue classes of integers with a fixed sum of digits</a>, The Ramanujan Journal, Vol. 9, No. 1-2 (2005), pp. 45-62; <a href="https://math.dartmouth.edu/~carlp/PDF/sarkozy06252003.pdf">alternative link</a>.
%H A094387 Michel Olivier, <a href="https://gallica.bnf.fr/ark:/12148/bpt6k62266732/f25.item">Sur la probabilité que n soit premier à la somme de ses chiffres</a>, C. R. Math. Acad. Sci. Paris, Série A, Vol. 280 (1975), pp. 543-545.
%H A094387 Michel Olivier, <a href="http://doi.org/10.4064/aa-31-4-361-384">Fonctions g-additives et formule asymptotique pour la propriété (n, f(n)) = q</a>, Acta Arithmetica, Vol. 31, No. 4 (1976), pp. 361-384; <a href="https://eudml.org/doc/205520">alternative link</a>.
%t A094387 Select[Range[100], CoprimeQ[#, DigitCount[#, 2, 1]] &] (* _Amiram Eldar_, Nov 22 2020 *)
%o A094387 (PARI) lista(nn) = {for (n=1, nn, if (gcd(n, norml2(binary(n))) == 1, print1(n, ", ")););} \\ _Michel Marcus_, May 25 2013
%o A094387 (Python)
%o A094387 from math import gcd
%o A094387 def ok(n): return gcd(n, bin(n).count('1')) == 1
%o A094387 print([k for k in range(104) if ok(k)]) # _Michael S. Branicky_, Jan 25 2022
%Y A094387 Cf. A000120, A059956.
%K A094387 nonn,base
%O A094387 1,2
%A A094387 _Benoit Cloitre_, Jun 08 2004