cp's OEIS Frontend

A293198 a(n) is the least positive k such that f(k) = f(k + n) where f(k) = A000120(k) / A070939(k).

%I A293198 #40 May 04 2021 12:15:37
%S A293198 1,5,1,9,3,21,1,2,2,19,2,38,3,37,1,33,15,35,38,37,84,35,76,12,7,10,9,
%T A293198 10,3,4,1,10,4,2,5,2,2,6,5,2,2,5,2,9,4,6,5,2,2,5,2,6,5,5,2,5,7,137,
%U A293198 138,134,3,133,1,129,63,131,134,133,140,131,138,137,152,139,134,133,148,131,146,56,336,135,150,52
%N A293198 a(n) is the least positive k such that f(k) = f(k + n) where f(k) = A000120(k) / A070939(k).
%C A293198 Numbers m such that a(2^m*(2^(m + 1) - 1) + 1) = 2^m are 0, 1, 2, 3, 4, 5, 6, 8, 9, 11, 14, 15, 18, 20, 21, ...
%C A293198 Numbers t such that a(t) = 2 are 7, 8, 10, 33, 35, 36, 39, 40, 42, 47, 48, 50, ...
%C A293198 Numbers t such that a(t) > t are 0, 1, 3, 5, 9, 11, 13, 15, 17, 18, 19, 20, 21, ...
%H A293198 Rémy Sigrist, <a href="/A293198/b293198.txt">Table of n, a(n) for n = 0..8192</a>
%H A293198 Altug Alkan, <a href="/A293198/a293198.png">Line graph of a(n+1)-a(n) for n <= 2^13</a>
%H A293198 Altug Alkan, <a href="/A293198/a293198_1.png">A logarithmic scatterplot of a(n)</a>
%F A293198 a(n) <> n for all n >= 0.
%F A293198 a(n) <= 5*n for all n >= 1.
%F A293198 a(2^m - 1) = 1 for all m >= 1.
%F A293198 a(2^m - 2^2) = 2^2 - 1 for all m >= 3.
%F A293198 a(2^m - 2^3) = 2^3 - 1 for all m >= 5.
%F A293198 a(2^m - 2^4) = 2^4 - 1 for all m >= 7.
%F A293198 a(2^m - 2^5) = 2^5 - 1 for all m >= 10.
%F A293198 a(2^m - 2^6) = 2^6 - 1 for all m >= 13.
%F A293198 a(2^m - 2^7) = 2^7 - 1 for all m >= 17.
%F A293198 a(2^m - 2^8) = 2^8 - 1 for all m >= 21.
%F A293198 a(2^m - 2^9) = 2^9 - 1 for all m >= 26.
%F A293198 a(2^(p - 1)) = 2^(p - 1) - 1 and a(2^(p - 1) - 1) = 2^p + 1 for all primes p.
%F A293198 a(2^(p - 1) + 1) = 2^p + 3 for all primes p >= 5.
%e A293198 a(5) = 21 because 21 = 2^4 + 2^2 + 2^0, 21 + 5 = 2^4 + 2^3 + 2^1; A000120(21) / A070939(21) = A000120(21 + 5) / A070939(21 + 5) and 21 is the least number with this property.
%o A293198 (PARI) a(n) = {my(k=1); while (hammingweight(k+n)/#binary(k+n) != hammingweight(k) /#binary(k), k++); k;}
%Y A293198 Cf. A000120, A070939, A099245, A099246, A292895.
%K A293198 nonn,base,look,easy
%O A293198 0,2
%A A293198 _Altug Alkan_, Oct 05 2017