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A019566 The differences 1-1, 21-12, 321-123, ..., 10987654321-12345678910, 1110987654321-1234567891011, etc. 5

%I #25 Nov 22 2020 21:14:13

%S 0,9,198,3087,41976,530865,6419754,75308643,864197532,-1358024589,

%T -123580236690,-2345801446791,775432077543108,178553219976533007,

%U 27956332009875522906,3805734210999774512805,481583522109989673502704,58259362312008979572492603

%N The differences 1-1, 21-12, 321-123, ..., 10987654321-12345678910, 1110987654321-1234567891011, etc.

%C All terms are divisible by 9, cf. A083449. There is an increasingly longer subsequence of negative terms starting at each power of 10, namely for indices n = 10..12, 100..123, 1000..1234, etc. - _M. F. Hasler_, Nov 02 2016

%C Gupta (1988) calls these "unique numbers".

%D S. S. Gupta, Unique Numbers, Science Today, Jan 01 1988, India.

%H Alois P. Heinz, <a href="/A019566/b019566.txt">Table of n, a(n) for n = 1..350</a>

%H Shyam Sunder Gupta, <a href="http://www.shyamsundergupta.com/unique.htm">Unique Numbers</a>

%F a(n) = A000422(n) - A007908(n) = 9*A083449(n).

%p u:= proc(n) u(n):= `if`(n=1, 1, parse(cat(u(n-1), n))) end:

%p d:= proc(n) d(n):= `if`(n=1, 1, parse(cat(n, d(n-1)))) end:

%p a:= n-> d(n)-u(n):

%p seq(a(n), n=1..20); # _Alois P. Heinz_, Dec 06 2014

%t f[n_] := Block[ {a = "", k = 1}, While[k < n + 1, a = StringJoin[ ToString[k], a]; k++ ]; Return[ ToExpression[a] - ToExpression[ StringReverse[a]]]]; Table[ f[n], {n, 1, 17} ]

%o (PARI) A = vector(25); c = 1; f = 1; for (i = 2, 9, c = 10*c + i; f = f + i*10^(i - 1); A[i] = (f - c)); for (i = 10, 25, c = 100*c + i; f = f + i*10^(2*i - 11);; A[i] = (f - c)); A \\ - _David Wasserman_, Nov 09 2004

%o (PARI) apply( {A019566(n)=A000422(n)-A007908(n)}, [1..22]) \\ Replacing code from Jan 13 2013, following a comment from Nov 02 2016. - _M. F. Hasler_, Nov 07 2020

%Y Cf. A000422, A007908.

%K sign,base,easy

%O 1,2

%A _Robert Dickau_

%E More terms from _Robert G. Wilson v_, Jan 11 2002

%E More terms from _David Wasserman_, Nov 09 2004

%E Edited by _N. J. A. Sloane_, Nov 22 2020

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)