A248014 -id:A248014 - cp's OEIS frontend

A248013 Numbers m such that A247796(m) = m.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 28, 29, 37, 38, 39, 46, 47, 48, 49, 55, 56, 57, 58, 59, 64, 65, 66, 67, 68, 69, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99, 191, 192, 193, 194, 195, 196, 197, 198, 199, 282

Offset: 1

Reinhard Zumkeller, Oct 08 2014

A247796(a(n)) = a(n);

numbers, containing no pair of adjacent digits with sum <= 9 in decimal representation.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A248014 (complement).

a248013 n = a248013_list !! (n-1)
a248013_list = filter (\x -> a247796 x == x) [0..]

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.

Original entry on oeis.org

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

Reinhard Zumkeller, Oct 08 2014

			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).

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

Cf. A248013, A248014.

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

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

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).

Edited by M. F. Hasler, Jan 29 2018

cp's OEIS Frontend

A248013 Numbers m such that A247796(m) = m.

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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.

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