A329623 - OEIS

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A329623

The absolute value of the difference between n and A053392(n), the concatenation of the sums of every pair of consecutive digits of n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 63

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

As A040115 forms the basis of an iterative sequence leading to A329200 and A329201, this sequence forms the basis of a similar sequence A329624. As the concatenation of the digit sum can lead to a value larger than the original term we must take the absolute value of the difference to ensure subsequent terms are always positive. The largest value in the first 10000 terms is a(9991) = 171819.

LINKS

Scott R. Shannon, Table of n, a(n) for n = 0..10000

EXAMPLE

a(9) = 9 as A053392(9) = 0 and | 9 - 0 | = 9.

a(10) = 10 as A053392(10) = 1 and | 10 - 1 | = 9.

a(100) = 90 as A053392(100) = 10 and | 100 - 10 | = 90.

a(119) = 91 as A053392(119) = 210 and | 119 - 210 | = 91.

MAPLE

A329623 := proc(n)

abs(n-A053392(n)) ;

end proc: # R. J. Mathar, Dec 11 2019

PROG