cp's OEIS Frontend

A275536 Differences of the exponents of the adjacent distinct powers of 2 in the binary representation of n (with -1 subtracted from the least exponent present) are concatenated as decimal digits in reverse order.

%I A275536 #40 Mar 19 2017 05:38:21
%S A275536 1,2,11,3,12,21,111,4,13,22,112,31,121,211,1111,5,14,23,113,32,122,
%T A275536 212,1112,41,131,221,1121,311,1211,2111,11111,6,15,24,114,33,123,213,
%U A275536 1113,42,132,222,1122,312,1212,2112,11112
%N A275536 Differences of the exponents of the adjacent distinct powers of 2 in the binary representation of n (with -1 subtracted from the least exponent present) are concatenated as decimal digits in reverse order.
%C A275536 A preferable representation is a sequence of arrays, since multi-digit items are possible: [1],[2],[1,1],[3],[1,2],[2,1],[1,1,1],[4],[1,3],[2,2],[1,1,2],[3,1],[1,2,1],[2,1,1],[1,1,1,1],[5],[1,4],[2,3],[1,1,3],[3,2],[1,2,2],[2,1,2],[1,1,1,2],[4,1],[1,3,1],[2,2,1],[1,1,2,1],[3,1,1],[1,2,1,1],[2,1,1,1],[1,1,1,1,1],[6],[1,5],[2,4],[1,1,4],[3,3],[1,2,3],[2,1,3],[1,1,1,3],[4,2],[1,3,2],[2,2,2],[1,1,2,2],[3,1,2],[1,2,1,2],[2,1,1,2],[1,1,1,1,2]. 0 is not allowed as a digit.
%C A275536 a(512) is the first term which cannot be expressed unambiguously in decimal. - _Charles R Greathouse IV_, Aug 02 2016
%C A275536 The first two terms which are equal (because of the ambiguity inherent in using decimal, or more generally any finite base) are a(3) = a(1024) = 11. a(3) corresponds to the array [1,1] while a(1024) corresponds to [11]. - _Charles R Greathouse IV_, Mar 19 2017
%H A275536 Charles R Greathouse IV, <a href="/A275536/b275536.txt">Table of n, a(n) for n = 1..511</a>
%F A275536 For n=1..511, a(n) = A004086(A004719(A071160(n))) [In other words, terms of A071160 with 0-digits deleted and the remaining digits reversed.] - _Antti Karttunen_, Sep 03 2016
%e A275536 5 = 2^2 + 2^0, so the representation is [2-0, 0-(-1)] = [2, 1] so a(5) = 12.
%e A275536 6 = 2^2 + 2^1, so the representation is [2-1, 1-(-1)] = [1, 2] so a(6) = 21.
%e A275536 18 = 2^4 + 2^1, so the representation is [4-1, 1-(-1)] = [3, 2] so a(18) = 23.
%o A275536 (PHP) function dec2delta($k) {
%o A275536   $p = -1;
%o A275536   while ($k > 0) {
%o A275536     $k -= $c = pow(2, floor(log($k, 2)));
%o A275536     if ($p > -1) $d[] = $p - floor(log($c, 2));
%o A275536     $p = floor(log($c, 2));
%o A275536   }
%o A275536   $d[] = $p + 1;
%o A275536   return array_reverse($d);
%o A275536 }
%o A275536 function delta2dec($d) {
%o A275536   $k = 0;
%o A275536   $e = -1;
%o A275536   foreach ($d AS $v) {
%o A275536     if ($v > 0) {
%o A275536       $e += $v;
%o A275536       $k += pow(2, $e);
%o A275536     }
%o A275536   }
%o A275536   return $k;
%o A275536 }
%o A275536 (PARI) a(n)=my(v=List(),k); while(n, k=valuation(n,2)+1; n>>=k; listput(v,k)); fromdigits(Vec(v)) \\ _Charles R Greathouse IV_, Aug 02 2016
%Y A275536 Cf. A069800, A261300, A248646, A256494, A258055, A004086, A004719, A071160.
%K A275536 nonn,base,fini
%O A275536 1,2
%A A275536 _Armands Strazds_, Aug 01 2016