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

Author

Reinhard Zumkeller, Oct 08 2014

Keywords

• nonn
• base
• look

Examples

			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).
		

Links

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

Crossrefs

Cf. A248013, A248014.

Programs

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

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).

Extensions

Edited by M. F. Hasler, Jan 29 2018