A235049 Subtract one from each nonzero digit in decimal representation of n.

0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60

Offset

0,4

Comments

Contains exactly the same terms as A007095, except that each occurs an infinite number of times.

A102683(a(n)) = 0. - Reinhard Zumkeller, Apr 16 2014

Links

Antti Karttunen, Table of n, a(n) for n = 0..10000

Index entries for sequences related to decimal expansion of n

Formula

a(0) = 0, and for n>=1, if n = 0 modulo 10, a(n) = 10*a(n/10), otherwise a(n) = 10*a(floor(n/10)) + (n modulo 10) - 1.

Example

Subtracting one from each nonzero digit of '9', we get 8, thus a(9)=8. Doing same for '10' results '00' thus a(10)=0. For '12', this results '01', thus a(12)=1.

Mathematica

a[n_] := FromDigits[If[#>0, #-1, #]& /@ IntegerDigits[n]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jan 13 2023 *)

Prog

(MIT/GNU Scheme, two implementations)
(define (A235049 n) (let loop ((z 0) (i 0) (n n)) (if (zero? n) z (let ((d (modulo n 10))) (loop (+ z (* (expt 10 i) (if (zero? d) d (- d 1)))) (1+ i) (floor->exact (/ n 10)))))))
;; As a recurrence, using memoization macro definec from Antti Karttunen's IntSeq-library:
(definec (A235049 n) (if (zero? n) n (let ((d (modulo n 10))) (+ (* 10 (A235049 (floor->exact (/ n 10)))) (if (zero? d) d (- d 1))))))
(Haskell)
a235049 x = if x == 0 then 0 else 10 * a235049 x' + max 0 (d - 1)
            where (x', d) = divMod x 10
-- Reinhard Zumkeller, Apr 16 2014

Crossrefs

Cf. A007095.

Sequence in context: A037851 A037887 A207505 * A031087 A010878 A309788

Adjacent sequences: A235046 A235047 A235048 * A235050 A235051 A235052

Keyword

nonn,easy,base,look

Author

Antti Karttunen, Apr 14 2014

Status

approved