A116303 -id:A116303 - cp's OEIS frontend

A116172 Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 5.

2, 74, 59264, 510782, 906902, 81790664, 92776472, 10876856041862, 11796926254874, 18332259798794, 18388650720624, 32624670587648, 32699883214248, 43103618706398, 44916698243804, 66132258426302

Offset: 1

Giovanni Resta, Feb 06 2006

Also numbers k such that k concatenated with k+6 gives the product of two numbers which differ by 3.
Also numbers k such that k concatenated with k+8 gives the product of two numbers which differ by 1.
If k+2 and k-4 have the same number of digits, then k is also in A116132 because k//k+2 = 10^d*k + k + 2 = m*(m+5) then implies k//k-4 = 10^d*k + k - 4 = m*(m+5) - 6 = (m-1)*(m+6). - R. J. Mathar, Aug 10 2008

			92776472//92776474 = 96320542 * 96320547, where // denotes concatenation.
92776472//92776480 = 96320544 * 96320545.
92776472//92776478 = 96320543 * 96320546.

Cf. A116158, A116171, A116173, A116179, A116303.

Cf. A116185, A115430, A116205, A116343, A116200, A116330.

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

A116304 Numbers k such that k*(k+6) gives the concatenation of two numbers m and m+2.

Original entry on oeis.org

8217107, 8030443878983905981, 43467818511541680701794365325328847002051, 56532181488458319298205634674671152997944

Offset: 1

Giovanni Resta, Feb 06 2006

			8217107 * 8217113 = 6752089//6752091, where // denotes concatenation.

Cf. A116173, A116290, A116303, A116305, A116318.

A116302 Numbers k such that k*(k+3) gives the concatenation of two numbers m and m+2.

Original entry on oeis.org

27, 71, 79822844, 69852478553064869297984899963806, 77473062193002372448027740546438, 77747359197583788609974143907618, 84341826458653210947638195982114, 85367942837521291760016984490250

Offset: 1

Giovanni Resta, Feb 06 2006

			79822844 * 79822847 = 63716866//63716868, where // denotes concatenation.

Cf. A116171, A116296, A116301, A116303, A116309.

A116310 n times n+5 gives the concatenation of two numbers m and m+3.

Original entry on oeis.org

2, 4, 88, 3676, 6320, 8786, 48743, 51253, 87617, 3762554, 6237442, 9217100, 3266298274, 3520463764, 6479536232, 6733701722, 8063694648, 8317860138, 4689524709430934474, 5310475290569065522, 7416797436703661747

Offset: 1

Giovanni Resta, Feb 06 2006

Cf. A116179, A116303, A116309, A116311, A116324.

cp's OEIS Frontend

A116172 Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 5.

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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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A116304 Numbers k such that k*(k+6) gives the concatenation of two numbers m and m+2.

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A116302 Numbers k such that k*(k+3) gives the concatenation of two numbers m and m+2.

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A116310 n times n+5 gives the concatenation of two numbers m and m+3.

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