A116162 -id:A116162 - cp's OEIS frontend

A116169 Numbers k such that k concatenated with k+1 gives the product of two numbers which differ by 9.

9, 49, 1166975893986638437392162264780939, 1411174268292962563778302427727571, 1860631503683565562655236868895135

Offset: 1

Giovanni Resta, Feb 06 2006

Also numbers k such that k concatenated with k+9 gives the product of two numbers which differ by 7.

			49//50 = 66 * 75, where // denotes concatenation.
49//58 = 67 * 74.

Cf. A116162, A116168, A116175, A116300.

Cf. A116215, A116174, A116223, A116353.

Edited by N. J. A. Sloane, Apr 15 2007

A116153 Numbers k such that k concatenated with k-1 gives the product of two numbers which differ by 9.

Original entry on oeis.org

13, 41, 653, 2287, 2723, 5491, 23240971, 26823191, 60249661, 1841968537, 2009317771, 3044234903, 3258336353, 8166731261, 9481619237, 1281071245505271100098621541, 1551605670846640136726379653

Offset: 1

Giovanni Resta, Feb 06 2006

Cf. A116147, A116152, A116162, A116284.

A116161 Numbers k such that k concatenated with itself gives the product of two numbers which differ by 8.

Original entry on oeis.org

3, 93, 145, 384, 505, 820, 993, 7680, 9993, 20665, 29748, 99993, 480340, 999993, 6694209, 9999993, 77854665, 99999993, 107541513, 109342209, 132231408, 174990384, 183673473, 213017748, 289940833, 326530608, 338353345

Offset: 1

Giovanni Resta, Feb 06 2006

Cf. A116146, A116160, A116162, A116168, A116292.

A116293 Numbers k such that k * (k+9) is the concatenation of a number m with itself.

Original entry on oeis.org

2, 92, 420, 572, 693, 728, 992, 9855, 9992, 36355, 63637, 99992, 970298, 999992, 4545455, 5454537, 9999992, 88235295, 99999992, 351069983, 403018035, 493927126, 506072866, 596981957, 648930009, 736842097, 739839100, 766233767, 769230761, 827751188, 857142858, 860139852, 879699240, 909090910

Offset: 1

Giovanni Resta, Feb 06 2006

From Robert Israel, Apr 09 2025: (Start)
Numbers k such that k * (k + 9) = (10^d + 1) * m for some d and m where m has d digits.
Contains 10^d-8 for all d >= 1. (End)

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A116162, A116284, A116292, A116300.

q:= proc(d,m) local R,t,a,b,x,q;
   t:= 10^d+1;
   R:= NULL;
   for a in numtheory:-divisors(t) do
     b:= t/a;
     if igcd(a,b) > 1 then next fi;
     for x from chrem([0,-m],[a,b]) by t do
       q:= x*(x+m)/t;
       if q >= 10^d then break fi;
       if q >= 10^(d-1) then R:= R, x fi;
   od od;
   sort(convert({R},list));
end proc:
seq(op(q(d,9)),d=1..10)

Name edited and more terms from Robert Israel, Apr 09 2025

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A116169 Numbers k such that k concatenated with k+1 gives the product of two numbers which differ by 9.

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A116153 Numbers k such that k concatenated with k-1 gives the product of two numbers which differ by 9.

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A116161 Numbers k such that k concatenated with itself gives the product of two numbers which differ by 8.

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A116293 Numbers k such that k * (k+9) is the concatenation of a number m with itself.

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