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

0, 9, 198, 3087, 41976, 530865, 6419754, 75308643, 864197532, -1358024589, -123580236690, -2345801446791, 775432077543108, 178553219976533007, 27956332009875522906, 3805734210999774512805, 481583522109989673502704, 58259362312008979572492603

Offset

1,2

Comments

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

Gupta (1988) calls these "unique numbers".

References

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

Links

Alois P. Heinz, Table of n, a(n) for n = 1..350

Shyam Sunder Gupta, Unique Numbers

Formula

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

Maple

u:= proc(n) u(n):= `if`(n=1, 1, parse(cat(u(n-1), n))) end:
d:= proc(n) d(n):= `if`(n=1, 1, parse(cat(n, d(n-1)))) end:
a:= n-> d(n)-u(n):
seq(a(n), n=1..20);  # Alois P. Heinz, Dec 06 2014

Mathematica

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} ]

Prog

(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
(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

Crossrefs

Cf. A000422, A007908.

Sequence in context: A291974 A180778 A110807 * A338226 A157563 A003026

Adjacent sequences: A019563 A019564 A019565 * A019567 A019568 A019569

Keyword

sign,base,easy

Author

Robert Dickau

Extensions

More terms from Robert G. Wilson v, Jan 11 2002

More terms from David Wasserman, Nov 09 2004

Edited by N. J. A. Sloane, Nov 22 2020

Status

approved