A115439 -id:A115439 - cp's OEIS frontend

A115428 Numbers k such that the concatenation of k with k+5 gives a square.

1, 4, 20, 31, 14564, 38239, 69919, 120395, 426436, 902596, 7478020, 9090220, 6671332084, 8114264059, 8482227259, 9900250996, 2244338786836, 2490577152964, 2509440638591, 2769448208395, 7012067592220

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 4.

Also numbers k such that k concatenated with k+4 gives the product of two numbers which differ by 2.

			14564_14569 = 38163^2.

Cf. A030465, A102567, A115426, A115437, A115429, A115430, A115431, A115432, A115433, A115434, A115435, A115436, A115439.

Cf. A116125, A116099, A116167, A116297, A116177, A116171, A116185, A116315.

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

A115446 Numbers k such that the square of k is the concatenation of two numbers m and m-8.

Original entry on oeis.org

4623, 5378, 7981, 34953, 46866, 53135, 65048, 7056187, 9783460, 43176671, 56823330, 97999801, 447255476453, 552744523548, 755424659535, 799319866014, 997999998001, 4297663349524, 5702336650477, 6971253996228, 7574200549228, 8843117894979, 3505613322543666, 3757750389995601, 3948262973033353

Offset: 1

Giovanni Resta, Jan 25 2006

			18642249_18642241 = 43176671^2.

David A. Corneth, Table of n, a(n) for n = 1..1730

Cf. A030467, A106497, A115435, A115427, A115438, A115439, A115440, A115441, A115442, A115443, A115444, A115445, A115447.

More terms from David A. Corneth, Jan 02 2021

A115427 Numbers k such that k^2 is the concatenation of two numbers m and m+2.

Original entry on oeis.org

8874, 9011, 83352842, 99000101, 329767122288, 670232877713, 738226276373, 933006600341, 999000001001, 3779410975143115, 3872816717528067, 4250291784692550, 4278630943941867, 4372036686326819, 4749511753491302

Offset: 1

Giovanni Resta, Jan 24 2006

			9011^2 = 8119_8121.

Cf. A030467, A106497, A115426, A115438, A115439, A115440, A115441, A115442, A115443, A115444, A115445, A115446, A115447.

A115438 Numbers whose square is the concatenation of two numbers k and k+4.

Original entry on oeis.org

2, 310, 453, 548, 691, 856, 4382, 5619, 72730, 346533, 653468, 9090908, 94117646, 334665333, 336032387, 378253328, 390977442, 439928491, 483516486, 516483515, 560071510, 609022559, 621746673, 663967614, 665334668

Offset: 1

Giovanni Resta, Jan 24 2006

From Farideh Firoozbakht, Nov 26 2006: (Start)
1. All numbers of the form f(n)=3(n).4.6(n).5.3(n+1) are in the sequence because if k(n)=1(n).2.0(n+1).8(n).5 then f(n)^2= k(n).(k(n)+4). For example f(3)=333466653333; k(3)=111200008885 and f(3)^2=333466653333^2=k(3).(k(3)+4)=111200008885.111200008889.
2. All numbers of the form g(n)=6(n).5.3(n).4.6(n).8 are in the sequence because g(0)=548 is in the sequence(548^2=300.304) and for n>0 if h(n)=4(n).2.6(n-1).70.2(n).0 then g(n)^2=h(n).(h(n)+4). For example g(5)=666665333334666668; h(5)=444442666670222220 and g(5)^2=h(5).(h(5)+4)=444442666670222220.444442666670222224. (End)

			120085_120089 = 346533^2.

Cf. A030467, A106497, A115437, A115427, A115439, A115440, A115441, A115442, A115443, A115444, A115445, A115446, A115447.

The initial "2" (which is admittedly somewhat dubious) added by N. J. A. Sloane, Aug 13 2008

A115440 Numbers whose square is the concatenation of two numbers k and k+8.

Original entry on oeis.org

7747, 8021, 33294318, 66705683, 98000201, 340465755425, 476452552745, 523547447256, 659534244576, 866013200681, 998000002001, 3695104677080134, 3755782995538768, 4198081170077531, 4803478892324966, 5196521107675035

Offset: 1

Giovanni Resta, Jan 24 2006

			6001_6009 = 7747^2.

Cf. A030467, A106497, A115429, A115427, A115438, A115439, A115441, A115442, A115443, A115444, A115445, A115446, A115447.

A115441 Numbers whose square is the concatenation of two numbers k and k+9.

Original entry on oeis.org

465, 536, 718, 822, 3428, 6573, 90907, 980202, 3636361, 6363640, 41176468, 58823533, 413533838, 426573430, 428571426, 432620009, 567379992, 571428575, 573426571, 586466163, 686261111, 725274729, 727272725, 731321308

Offset: 1

Giovanni Resta, Jan 24 2006

			82640_82649 = 90907^2.

Cf. A030467, A106497, A115430, A115427, A115438, A115439, A115440, A115442, A115443, A115444, A115445, A115446, A115447.

A115442 Numbers whose square is the concatenation of two numbers k and k-2.

Original entry on oeis.org

8, 7312, 8991, 32524, 67477, 76568, 4891730, 5108271, 8528094, 71588336, 98999901, 399659933007, 600340066994, 723627738227, 877712329768, 998999999001, 3485626998114, 3787100274614, 6212899725387, 6514373001887

Offset: 1

Giovanni Resta, Jan 24 2006

			8083_8081 = 8991^2.

Cf. A030467, A106497, A115431, A115427, A115438, A115439, A115440, A115441, A115443, A115444, A115445, A115446, A115447.

Select[Table[Sqrt[k*10^IntegerLength[k]+k-2],{k,4,86*10^5}],IntegerQ] (* The program generates the first 9 terms of the sequence. *) (* Harvey P. Dale, Nov 02 2024 *)

A115443 Numbers whose square is the concatenation of two numbers k and k-4.

Original entry on oeis.org

81, 8157, 9801, 467347, 532654, 998001, 76450589, 99980001, 7801738415, 8593817623, 9208120793, 9999800001, 346667333467, 401461854015, 598538145986, 653332666534, 945207479453, 999998000001, 48349470735060

Offset: 1

Giovanni Resta, Jan 25 2006

			9605_9601 = 9801^2.

Cf. A030467, A106497, A115432, A115427, A115438, A115439, A115440, A115441, A115442, A115444, A115445, A115446, A115447.

A115444 Numbers whose square is the concatenation of two numbers k and k-5.

Original entry on oeis.org

46, 55, 949951, 979654, 7771781679, 7900890080, 9920892100, 9949999501, 38773083432317, 41534158410842, 47433813119408, 52566186880593, 58465841589159, 61226916567684, 72258945037435, 86156896546725

Offset: 1

Giovanni Resta, Jan 25 2006

			902406_902401 = 949951^2.

Cf. A030467, A106497, A115433, A115427, A115438, A115439, A115440, A115441, A115442, A115443, A115445, A115446, A115447.

A115445 Numbers whose square is the concatenation of two numbers k and k-7.

Original entry on oeis.org

9, 13, 3656545, 4565636, 5434365, 6343456, 3646962589704198389, 6353037410295801612, 9101508044249652935, 7903999111431765764698711045778, 9722180929613583946516892863960

Offset: 1

Giovanni Resta, Jan 25 2006

			4023943_4023936 = 6343456^2.

Cf. A030467, A106497, A115434, A115427, A115438, A115439, A115440, A115441, A115442, A115443, A115444, A115446, A115447.

cp's OEIS Frontend

A115428 Numbers k such that the concatenation of k with k+5 gives a square.

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A115446 Numbers k such that the square of k is the concatenation of two numbers m and m-8.

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A115427 Numbers k such that k^2 is the concatenation of two numbers m and m+2.

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A115438 Numbers whose square is the concatenation of two numbers k and k+4.

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A115440 Numbers whose square is the concatenation of two numbers k and k+8.

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A115441 Numbers whose square is the concatenation of two numbers k and k+9.

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A115442 Numbers whose square is the concatenation of two numbers k and k-2.

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A115443 Numbers whose square is the concatenation of two numbers k and k-4.

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A115444 Numbers whose square is the concatenation of two numbers k and k-5.

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A115445 Numbers whose square is the concatenation of two numbers k and k-7.

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