A116281 -id:A116281 - cp's OEIS frontend

A116112 Numbers k such that k concatenated with k-7 gives the product of two numbers which differ by 7.

17, 35, 10408517, 45884051, 62918301, 1116290522645838319925, 1491109615209578451401, 2254276950187476704727, 2758431647767103545151, 3768131911733856383477, 4434103687048263321737, 5230580700713956424051

Offset: 1

Giovanni Resta, Feb 06 2006

Also numbers k such that k concatenated with k-1 gives the product of two numbers which differ by 5.
Also numbers k such that k concatenated with k+3 gives the product of two numbers which differ by 3.
Also numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 1.

			62918301//62918300 = 79321055 * 79321060, where // denotes concatenation.
62918301//62918304 = 79321056 * 79321059.
62918301//62918306 = 79321057 * 79321058.

Cf. A116107, A115426, A116113, A116119, A116243.
Cf. A116163, A115429, A116158, A116281.
Cf. A116171, A116177, A116179, A116185, A116309, A115430, A116322.

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

A116289 Numbers k such that k*(k+5) gives the concatenation of a number m with itself.

Original entry on oeis.org

6, 96, 385, 429, 567, 611, 814, 996, 4521, 5475, 9996, 90910, 99996, 316832, 683164, 999996, 3636364, 6363632, 9999996, 82352942, 99999996, 331668332, 368421053, 395604391, 442767754, 461538462, 488721800, 511278196, 538461534, 557232242, 604395605, 631578943, 668331664, 700089385, 727272728

Offset: 1

Giovanni Resta, Feb 06 2006

From Robert Israel, Apr 09 2025: (Start)
Numbers k such that k * (k + 5) = (10^d + 1) * m for some d and m where m has d digits.
Contains 10^d-4 for all d >= 1. (End)

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

Cf. A028557, A020338.

Cf. A116158, A116281, A116288, A116290, A116303.

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,5)),d=1..10); # Robert Israel, Apr 09 2025

More terms from Robert Israel, Apr 09 2025

A116276 Numbers k such that k*(k+5) gives the concatenation of two numbers m and m-2.

Original entry on oeis.org

70, 79822843, 69852478553064869297984899963805, 77473062193002372448027740546437, 77747359197583788609974143907617, 84341826458653210947638195982113, 85367942837521291760016984490249

Offset: 1

Giovanni Resta, Feb 06 2006

			79822843 * 79822848 = 63716866//63716864, where // denotes concatenation.

Cf. A028557, A116107, A116268, A116275, A116277, A116281.

A116280 n times n+3 gives the concatenation of two numbers m and m-1.

Original entry on oeis.org

6, 77, 80918, 91808, 326509, 475024, 524974, 673489, 4323776, 4767131, 5232867, 5676222, 4083911140, 4975000249, 5024999749, 5916088858, 9503960495, 9604950395, 4186904462791, 4313465946774, 5686534053224, 5813095537207

Offset: 1

Giovanni Resta, Feb 06 2006

Cf. A116149, A116274, A116279, A116281, A116287.

A116282 Numbers k such that k*(k+6) gives the concatenation of two numbers m and m-1.

Original entry on oeis.org

7744, 8018, 33294315, 66705680, 98000198, 340465755422, 476452552742, 523547447253, 659534244573, 866013200678, 998000001998, 3695104677080131, 3755782995538765, 4198081170077528, 4803478892324963, 5196521107675032

Offset: 1

Giovanni Resta, Feb 06 2006

			98000198 * 98000204 = 96040393//96040392, where // denotes concatenation.

Cf. A115429, A116262, A116281, A116283, A116290.

cp's OEIS Frontend

A116112 Numbers k such that k concatenated with k-7 gives the product of two numbers which differ by 7.

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A116289 Numbers k such that k*(k+5) gives the concatenation of a number m with itself.

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A116276 Numbers k such that k*(k+5) gives the concatenation of two numbers m and m-2.

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A116280 n times n+3 gives the concatenation of two numbers m and m-1.

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A116282 Numbers k such that k*(k+6) gives the concatenation of two numbers m and m-1.

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