A116172 -id:A116172 - cp's OEIS frontend

A115430 Numbers k such that the concatenation of k with k+9 gives a square.

216, 287, 515, 675, 1175, 4320, 82640, 960795, 1322312, 4049591, 16955015, 34602080, 171010235, 181964891, 183673467, 187160072, 321920055, 326530616, 328818032, 343942560, 470954312, 526023432, 528925616, 534830855

Offset: 1

Giovanni Resta, Jan 24 2006

Also numbers k such that k concatenated with k+8 gives the product of two numbers which differ by 2.

Also numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 4.

			82640_82649 = 90907^2.

Cf. A030465, A102567, A115426, A115437, A115428, A115429, A115431, A115432, A115433, A115434, A115435, A115436, A115441.

Cf. A116172, A116168, A116344, A116112, A116193, A116173, A116323.

Edited by N. J. A. Sloane, Apr 13 2007

A116205 Numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 3.

Original entry on oeis.org

1, 81, 1353, 3997, 7723, 23761, 26271, 76771, 1415683, 3890571, 8495497, 1066870443, 1239366513, 4198438981, 4534273891, 6502317141, 6918679731, 2199164200036329043, 2820114781174460091, 5500888421709400741

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 1.

Also numbers k such that k concatenated with k-3 gives the product of two numbers which differ by 7.

Cf. A116179, A116172, A115429, A116173, A116193, A116336.

Cf. A116132, A116099, A116139, A116152, A116269, A116348.

Edited by N. J. A. Sloane, Apr 13 2007

A116173 Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 6.

Original entry on oeis.org

6752089, 6448802889351008245, 18894512461523256139943105859903480218905, 31958875438439894736354375209245786214798

Offset: 1

Giovanni Resta, Feb 06 2006

Also numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 4.

If k+2 and k-5 have the same number of digits, the k is also in A116126, because k//k+2 = 10^d*k + k + 2 = m*(m+6) then implies a representation k//k-5 = 10^d*k + k - 5 = m*(m+6)-7 = (m-1)*(m+7). - R. J. Mathar, Aug 10 2008

			6752089//6752091 = 8217107 * 8217113, where // denotes concatenation.
6752089//6752096 = 8217108 * 8217112.

Cf. A116159, A116172, A116174, A116187, A116304.

Cf. A115430, A116205, A116207, A116187, A116337.

Edited by N. J. A. Sloane, Apr 12 2007

A116171 Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 3.

Original entry on oeis.org

8, 52, 63716866, 48793687600063875363014809897052, 60020753655608135708762056127156, 60446518621981165303188950156776, 71135436903815748345367595855336, 72876856643103028189103298533248

Offset: 1

Giovanni Resta, Feb 06 2006

Also numbers k such that k concatenated with k+4 gives the product of two numbers which differ by 1.

			63716866//63716868 = 79822844 * 79822847, where // denotes concatenation.
63716866//63716870 = 79822845 * 79822846.

Cf. A116099, A116170, A116172, A116112, A116302, A116099, A115428, A116314.

Edited by N. J. A. Sloane, Apr 13 2007

A116179 Numbers k such that k concatenated with k+3 gives the product of two numbers which differ by 5.

Original entry on oeis.org

1, 3, 81, 1353, 3997, 7723, 23761, 26271, 76771, 1415683, 3890571, 8495497, 1066870443, 1239366513, 4198438981, 4534273891, 6502317141, 6918679731, 2199164200036329043, 2820114781174460091, 5500888421709400741

Offset: 1

Giovanni Resta, Feb 06 2006

Cf. A116172, A116112, A116180, A116193, A116310.

A116185 Numbers k such that k concatenated with k+4 gives the product of two numbers which differ by 3.

Original entry on oeis.org

150, 186, 324, 376, 666, 2046, 3000, 82650, 100384, 466716, 1322316, 4049584, 67820074, 110003884, 135734074, 156502836, 196043286, 213017754, 238849000, 261405396, 289940826, 310507774, 365294050, 398891964, 446667216

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 1.

Cf. A116112, A115428, A115429, A116316, A116199, A116172, A116329.

cc:=proc(x,y) local s: s:=proc(m) nops(convert(m,base,10)) end: x*10^s(y)+y: end: a:=proc(n) if type(sqrt(9+4*cc(n,n+4)),integer) then n else fi end: seq(a(n),n=1..500000); # very slow; cc yields the concatenation of x and y; - Emeric Deutsch, May 05 2007

Edited by N. J. A. Sloane, Apr 14 2007

A116158 Numbers k such that k concatenated with itself gives the product of two numbers which differ by 5.

Original entry on oeis.org

6, 96, 150, 186, 324, 376, 666, 996, 2046, 3000, 9996, 82650, 99996, 100384, 466716, 999996, 1322316, 4049584, 9999996, 67820074, 99999996, 110003884, 135734074, 156502836, 196043286, 213017754, 238849000, 261405396

Offset: 1

Giovanni Resta, Feb 06 2006

Cf. A116112, A116125, A116159, A116172, A116289.

A116200 Numbers k such that k concatenated with k+6 gives the product of two numbers which differ by 5.

Original entry on oeis.org

210, 294, 5880, 52888, 127044, 414180, 8264470, 12456750, 41868508, 112670544, 441341880, 468144040, 669421494, 702338994, 715976338, 750005718, 960645294, 1491030294, 3768258010, 4783279044, 8505429358, 17105045530

Offset: 1

Giovanni Resta, Feb 06 2006

Cf. A116193, A116172, A116147, A116207, A116331.

A116303 n times n+5 gives the concatenation of two numbers m and m+2.

Original entry on oeis.org

3, 84, 76981, 714688, 952312, 90438189, 96320542, 32980078899027, 34346653774236, 42816188292271, 42881990066486, 57118009933510, 57183811707725, 65653346225760, 67019921100969, 81321742742208

Offset: 1

Giovanni Resta, Feb 06 2006

			96320542 * 96320547 = 92776472//92776474, where // denotes
concatenation.

Cf. A116172, A116289, A116302, A116304, A116310.

A116330 Numbers k such that k*(k+3) gives the concatenation of two numbers m and m+6.

Original entry on oeis.org

4, 85, 76982, 714689, 952313, 90438190, 96320543, 32980078899028, 34346653774237, 42816188292272, 42881990066487, 57118009933511, 57183811707726, 65653346225761, 67019921100970, 81321742742209

Offset: 1

Giovanni Resta, Feb 06 2006

			96320543 * 96320546 = 92776472//92776478, where // denotes concatenation.

Cf. A116172, A116316, A116329, A116331, A116336.

cp's OEIS Frontend

A115430 Numbers k such that the concatenation of k with k+9 gives a square.

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A116205 Numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 3.

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A116173 Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 6.

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A116171 Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 3.

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A116179 Numbers k such that k concatenated with k+3 gives the product of two numbers which differ by 5.

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A116185 Numbers k such that k concatenated with k+4 gives the product of two numbers which differ by 3.

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A116158 Numbers k such that k concatenated with itself gives the product of two numbers which differ by 5.

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A116200 Numbers k such that k concatenated with k+6 gives the product of two numbers which differ by 5.

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A116303 n times n+5 gives the concatenation of two numbers m and m+2.

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A116330 Numbers k such that k*(k+3) gives the concatenation of two numbers m and m+6.

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