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A355675 a(0) = 0, and for any n > 0 and d = 1..9, a(10*n) = 10*a(n), a(10*n + d) = d - 10*a(n).

%I A355675 #10 Jul 18 2022 14:16:45
%S A355675 0,1,2,3,4,5,6,7,8,9,10,-9,-8,-7,-6,-5,-4,-3,-2,-1,20,-19,-18,-17,-16,
%T A355675 -15,-14,-13,-12,-11,30,-29,-28,-27,-26,-25,-24,-23,-22,-21,40,-39,
%U A355675 -38,-37,-36,-35,-34,-33,-32,-31,50,-49,-48,-47,-46,-45,-44,-43,-42
%N A355675 a(0) = 0, and for any n > 0 and d = 1..9, a(10*n) = 10*a(n), a(10*n + d) = d - 10*a(n).
%C A355675 This sequence establishes a bijection from the nonnegative integers (N) to the integers (Z).
%C A355675 This sequence is to base 10 what A065620 is to base 2.
%C A355675 To compute a(n): write n a sum of terms of A037124 with distinct 10-adic valuations and take the alternating sum.
%C A355675 This sequence has similarities with A073835; they first differ in absolute value for n = 101: a(101) = 99 whereas A073835(101) = 101.
%C A355675 This sequence has similarities with A334387; they first differ in absolute value for n = 111: a(111) = 91 whereas A334387(111) = 81.
%H A355675 Rémy Sigrist, <a href="/A355675/b355675.txt">Table of n, a(n) for n = 0..10000</a>
%H A355675 <a href="/index/De#decimal_expansion">Index entries for sequences related to decimal expansion of n</a>
%F A355675 a(n) = 0 iff n = 0 or n belongs to A037124.
%e A355675 For n = 17039:
%e A355675   17039 = 10000 + 7000 + 30 + 9,
%e A355675   so a(17039) = -10000 + 7000 - 30 + 9 = -3021.
%o A355675 (PARI) a(n, base=10) = { my (d=digits(n, base), s=1); forstep (k=#d, 1, -1, if (d[k], d[k]*=s; s=-s)); return (fromdigits(d, base)) }
%Y A355675 Cf. A037124, A065620, A073835, A334387, A355624.
%K A355675 sign,base,easy
%O A355675 0,3
%A A355675 _Rémy Sigrist_, Jul 14 2022