A080463 -id:A080463 - cp's OEIS frontend

A080464 Product of the two numbers formed by alternate digits of n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 0

Offset: 10

Amarnath Murthy, Mar 02 2003

			a(132546) = 124 * 356 = 44144.

M. F. Hasler, Table of n, a(n) for n = 10..10000

Cf. A007954, A080463, A080465, A087471, A087472, A087473, A087474.

nad[n_]:=Module[{idn=IntegerDigits[n]},FromDigits[Take[idn,{1,-1,2}]] FromDigits[ Take[idn,{2,-1,2}]]]; Array[nad,120,10] (* Harvey P. Dale, Aug 07 2019 *)

A080464(n,d=digits(n))={n=d*matrix(#d,2,z,s,if((z-s)%2,10^((#d-z)\2)));n[1]*n[2]}

a(n) < n for all n. - M. F. Hasler, Jan 10 2016

More terms from Ray Chandler, Oct 11 2003

A080465 Absolute difference between the two numbers formed by alternate digits of n.

Original entry on oeis.org

1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 9

Offset: 10

Amarnath Murthy, Mar 02 2003

Differs from A040115 first at a(110) = 9. - R. J. Mathar, Sep 19 2008

			a(132546) = |124 - 356| = 232.

T. D. Noe, Table of n, a(n) for n=10..10000

Cf. A080463, A080464, A267086.

A209685 Sum of last two digits of n.

Original entry on oeis.org

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

A267086 Numbers such that the number formed by digits in even positions divides, or is divisible by, the number formed by the digits in odd positions; zero allowed.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 28, 30, 31, 33, 36, 39, 40, 41, 42, 44, 48, 50, 51, 55, 60, 61, 62, 63, 66, 70, 71, 77, 80, 81, 82, 84, 88, 90, 91, 93, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 122, 124, 126, 128, 132, 135

Offset: 1

M. F. Hasler, Jan 10 2016

The initial 0 is included by convention. The single-digit numbers are included with the reasoning that the number formed by digits in even positions is zero, and thus divisible by (= a multiple of) any other number, and here in particular the number formed by first digit.
By "digits in odd positions" we mean the first (most significant), third, fifth, etc. digits; e.g., for the numbers 12345 or 123456 this would be 135.
An extended version of Eric Angelini's "integears" A267085.
Sequence A263314 is a subsequence up to 120, but 121 is in A263314 and not in this sequence.

			12 is in the sequence because 1 divides 2.
213 is in the sequence because 1 divides 23.
1020 is in the sequence because 12 divides 00 = 0. (Any number divides 0 therefore any number which has every other digit equal to zero is in the sequence.)

Robert Israel, Table of n, a(n) for n = 1..10000
E. Angelini, Integears, SeqFan list, Jan. 10, 2016.

Cf. A267085, A263314.

A267085 Numbers such that the number formed by digits in even position divides, or is divisible by, the number formed by the digits in odd position; both must be nonzero.

Original entry on oeis.org

11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 24, 26, 28, 31, 33, 36, 39, 41, 42, 44, 48, 51, 55, 61, 62, 63, 66, 71, 77, 81, 82, 84, 88, 91, 93, 99, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 122, 124, 126, 128, 132, 135, 138, 142, 146, 150, 155, 162, 168, 174, 186, 198

Offset: 1

Eric Angelini and M. F. Hasler, Jan 10 2016

Termed "integears" by Eric Angelini. See A267086 for the "extended version" where zero is allowed.

Michael De Vlieger, Table of n, a(n) for n = 1..10000
E. Angelini, Integears, SeqFan list, Jan. 10, 2016.

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A080464 Product of the two numbers formed by alternate digits of n.

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A080465 Absolute difference between the two numbers formed by alternate digits of n.

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A209685 Sum of last two digits of n.

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A267086 Numbers such that the number formed by digits in even positions divides, or is divisible by, the number formed by the digits in odd positions; zero allowed.

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A267085 Numbers such that the number formed by digits in even position divides, or is divisible by, the number formed by the digits in odd position; both must be nonzero.

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