# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a309648 Showing 1-1 of 1 %I A309648 #13 Aug 11 2019 16:18:04 %S A309648 3,8,3,1,2,9,6,6,6,3,4,7,2,1,2,7,3,2,8,8,9,6,6,7,5,4,3,4,6,3,4,6,6,6, %T A309648 2,4,7,5,2,4,9,7,0,9,3,2,9,1,1,3,3,2,9,8,7,5,4,6,7,1,3,0,2,6,8,3,3,0, %U A309648 4,9,8,3,5,3,1,9,6,1,4,0,3,8,6,4,6,2,0,2,7,6,3,3,0,9,9,9,4,6,2,2 %N A309648 Digits of the 10-adic integer (-17/9)^(1/3). %H A309648 Seiichi Manyama, Table of n, a(n) for n = 0..10000 %F A309648 Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 3, b(n) = b(n-1) + 3 * (9 * b(n-1)^3 + 17) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n. %e A309648 3^3 == 7 (mod 10). %e A309648 83^3 == 87 (mod 10^2). %e A309648 383^3 == 887 (mod 10^3). %e A309648 1383^3 == 8887 (mod 10^4). %e A309648 21383^3 == 88887 (mod 10^5). %e A309648 921383^3 == 888887 (mod 10^6). %o A309648 (PARI) N=100; Vecrev(digits(lift(chinese(Mod((-17/9+O(2^N))^(1/3), 2^N), Mod((-17/9+O(5^N))^(1/3), 5^N)))), N) %o A309648 (Ruby) %o A309648 def A309648(n) %o A309648 ary = [3] %o A309648 a = 3 %o A309648 n.times{|i| %o A309648 b = (a + 3 * (9 * a ** 3 + 17)) % (10 ** (i + 2)) %o A309648 ary << (b - a) / (10 ** (i + 1)) %o A309648 a = b %o A309648 } %o A309648 ary %o A309648 end %o A309648 p A309648(100) %Y A309648 Cf. A309600 %K A309648 nonn,base %O A309648 0,1 %A A309648 _Seiichi Manyama_, Aug 11 2019 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE