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

Offset: 0

Author

Scott R. Shannon, Nov 19 2019

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A040115, A053392, A053393, A329200, A329201, A329624.

Programs

Maple

A329623 := proc(n)
    abs(n-A053392(n)) ;
end proc: # R. J. Mathar, Dec 11 2019

PARI

A329623(n)=abs(n-A053392(n)) \\ M. F. Hasler, Dec 02 2019