A209674 -id:A209674 - cp's OEIS frontend

A209685 Sum of last two digits of n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1

Offset: 0

N. J. A. Sloane, Mar 11 2012

Note that "Sum of last three digits of n" takes the same values as this sequence for n <= 99 (but not for n = 100). "Sum of last three digits of n" repeats every 1000 terms, while this sequence repeats every 100 values. Analogs are obvious for "sum of the last 4 values of n" which repeats every 10^4 values. - Jonathan Vos Post, Mar 12 2012 [First sentence corrected by N. J. A. Sloane, Feb 12 2017]

			99->9+9=18, 100->0+0=0.

Indranil Ghosh, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. A209674, A080463. Differs from A007953 and A076314 at n=100.

a(n)=n%100\10+n%10 \\ Charles R Greathouse IV, Mar 11 2012

def A209685(n):
    if n<=9:return n
    return int(str(n)[-1])+int(str(n)[-2]) # Indranil Ghosh, Feb 12 2017

A209686 For each n, define a sequence of numbers by S(0)=n, S(i) = sum of last three digits of the concatenation S(0)S(1)S(2)...S(i-1); a(n) = smallest m such that S(m) = 11, or -1 if 11 is never reached.

Original entry on oeis.org

-1, 6, 8, 14, 7, 6, 13, 16, 6, 7, 5, 0, 3, 8, 6, 13, 16, 6, 7, 7, 15, 11, 7, 6, 13, 16, 6, 7, 9, 1, 9, 15, 6, 13, 16, 6, 7, 12, 1, 10, 4, 6, 13, 16, 6, 7, 9, 1, 2, 4, 6, 13, 16, 6, 7, 5, 1, 20, 13, -1, 13, 16, 6, 7, 4, 1, 12, 2, 5, 3, 16, 6, 7, 10, 1, 3, 11, 15, 6, 13, 6, 7, 19, 1, 14, 6, 2, 7, 5, 9, 7, 9, 1, 12, 4, 5

Offset: 0

N. J. A. Sloane, Mar 11 2012

			3->3->6->12->9->12->12->5->8->15->14->10->5->6->11, so a(3)=14.
59->14->14->9->14->14->9->... never reaches 11, so a(59)=-1.

Eric Angelini, Posting to Math Fun Mailing List, Mar 11 2012.

Cf. A209674.

cp's OEIS Frontend

A209685 Sum of last two digits of n.

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