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A113589 A complementary variation of 'n described': if n is read as "a ones b twos" then a(n) = "one a's two b's", etc.

%I A113589 #13 Jul 11 2022 02:39:08
%S A113589 0,1,11,111,1111,11111,111111,1111111,11111111,111111111,1,2,111,1111,
%T A113589 11111,111111,1111111,11111111,111111111,1111111111,11,111,22,11111,
%U A113589 111111,1111111,11111111,111111111,1111111111,11111111111,111,1111,11111,222
%N A113589 A complementary variation of 'n described': if n is read as "a ones b twos" then a(n) = "one a's two b's", etc.
%H A113589 Rémy Sigrist, <a href="/A113589/b113589.txt">Table of n, a(n) for n = 0..10000</a>
%F A113589 a(A002275(n)) = n. - _Rémy Sigrist_, Feb 09 2022
%e A113589 A045918(10) = 1110 = 'one one one zero', hence a(10) = 'one one, zero ones' = 1.
%e A113589 A045918(11) = 21 = 'two ones', hence a(11) = 'one twos' = 2.
%e A113589 a(123) = 111111.
%o A113589 (PARI) a(n) = { my (d=[]); while (n, my (t=n%10, k=0); while (n%10==t, n\=10; k++;); for (i=1, t, d=concat(digits(k), d))); fromdigits(d) } \\ _Rémy Sigrist_, Feb 09 2022
%Y A113589 Cf. A002275, A045918, A140057, A306366.
%K A113589 base,nonn,easy
%O A113589 0,3
%A A113589 _Amarnath Murthy_, Nov 07 2005
%E A113589 Extended and corrected by _Nathaniel Johnston_, Apr 29 2011
%E A113589 a(0) = 0 prepended by _Rémy Sigrist_, Feb 09 2022