A247796 From right to left in decimal representation of n: replace each maximal set of adjacent digits with their sum, if this sum is less than 10.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 2, 3, 4, 5, 6, 7, 8, 9, 28, 29, 3, 4, 5, 6, 7, 8, 9, 37, 38, 39, 4, 5, 6, 7, 8, 9, 46, 47, 48, 49, 5, 6, 7, 8, 9, 55, 56, 57, 58, 59, 6, 7, 8, 9, 64, 65, 66, 67, 68, 69, 7, 8, 9, 73, 74, 75, 76, 77

Offset

0,3

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Formula

a(n) <= n; a(A248013(n)) = A248013(n); a(A248014(n)) < A248014(n);

a(n) = a(a(n)) = a(A004719(n)) = a(n * 10^k).

Example

7654321: 7654[321] -> 7654[3+2+1] -> 76546 -> 76[54]6 -> 76[5+4]6 -> 7696 = a(7654321);
1234567: 123[45]67 -> 123[4+5]67 -> 123967 -> [123]967 -> [1+2+3]967 -> 6967 = a(1234567);
1111111: [1111111] -> [1+1+1+1+1+1+1] -> 7 = a(1111111);
a(7777777) = 7777777;
90909: 909[09] -> 909[0+9] -> 9099 -> 9[09]9 -> 9[0+9]9 -> 999 = a(90909);
20202: [20202] -> [2+0+2+0+2] -> 6 = a(20202).

Prog

(Haskell)
a247796 = f 0 where
   f s 0 = s
   f s x = if s + d < 10 then f (s + d) x' else (f d x') * 10 + s
           where (x', d) = divMod x 10
(PARI) A247796(n, d=digits(n))={forstep(k=#d, 2, -1, if(d[k-1]+d[k]<10, d[k-1]+=d[k]; d=d[^k])); fromdigits(d)} /* or: (about 10% faster) */
A247796(n, u=1)={until(n<10*u*=10, my(m=n\u); while(m>9&&sumdigits(m%100)<10, m=vecsum(divrem(m, 10)); n=m*u+n%u)); n} \\ Trying to reduce the number of redefinitions of n yields slower code. M. F. Hasler, Jan 29 2018

Crossrefs

Cf. A248013, A248014.

Sequence in context: A114570 A349194 A342829 * A355370 A326344 A340270

Adjacent sequences: A247793 A247794 A247795 * A247797 A247798 A247799

Keyword

nonn,base,look

Author

Reinhard Zumkeller, Oct 08 2014

Extensions

Edited by M. F. Hasler, Jan 29 2018

Status

approved