A020338 -id:A020338 - cp's OEIS frontend

A116160 Numbers k such that k concatenated with itself gives the product of two numbers which differ by 7.

4, 94, 210, 294, 994, 5880, 9994, 52888, 99994, 127044, 414180, 999994, 8264470, 9999994, 12456750, 41868508, 99999994, 112670544, 441341880, 468144040, 669421494, 702338994, 715976338, 750005718, 960645294, 999999994

Offset: 1

Giovanni Resta, Feb 06 2006

Cf. A020338, A116152, A116159, A116161, A116167, A116291.

A178664 a(n) = 2^n concatenated with itself.

Original entry on oeis.org

11, 22, 44, 88, 1616, 3232, 6464, 128128, 256256, 512512, 10241024, 20482048, 40964096, 81928192, 1638416384, 3276832768, 6553665536, 131072131072, 262144262144, 524288524288, 10485761048576, 20971522097152, 41943044194304, 83886088388608, 1677721616777216

Offset: 0

Vincenzo Librandi, Jul 10 2010

			a(1) = 22 because 2^1 concatenated with 2^1 is 22.

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Cf. A000079.

[Seqint(Intseq(2^n) cat Intseq(2^n)): n in [0..40]]; // Vincenzo Librandi, Mar 14 2012

a:= n-> parse(cat(2^n$2)):
seq(a(n), n=0..25);  # Alois P. Heinz, Jun 24 2025

Table[FromDigits[Join[IntegerDigits[2^n],IntegerDigits[2^n]]],{n,0,30}] (* Vincenzo Librandi, Mar 14 2012 *)
#*10^IntegerLength[#]+#&/@(2^Range[0,25]) (* Harvey P. Dale, Aug 29 2024 *)

a(n) = A020338(2^n). - Bruno Berselli, Mar 14 2012

A032610 Concatenation of n and n + 5 or {n,n+5}.

Original entry on oeis.org

16, 27, 38, 49, 510, 611, 712, 813, 914, 1015, 1116, 1217, 1318, 1419, 1520, 1621, 1722, 1823, 1924, 2025, 2126, 2227, 2328, 2429, 2530, 2631, 2732, 2833, 2934, 3035, 3136, 3237, 3338, 3439, 3540, 3641, 3742, 3843, 3944, 4045, 4146, 4247

Offset: 1

Patrick De Geest, May 15 1998

Cf. A001704, A020338.

A032612 Concatenation of n and n+7.

Original entry on oeis.org

18, 29, 310, 411, 512, 613, 714, 815, 916, 1017, 1118, 1219, 1320, 1421, 1522, 1623, 1724, 1825, 1926, 2027, 2128, 2229, 2330, 2431, 2532, 2633, 2734, 2835, 2936, 3037, 3138, 3239, 3340, 3441, 3542, 3643, 3744, 3845, 3946, 4047, 4148, 4249

Offset: 1

Patrick De Geest, May 15 1998

Cf. A001704, A020338.

Table[n*10^IntegerLength[n+7]+n+7,{n,50}] (* Harvey P. Dale, Apr 26 2025 *)

def A032612(n): return n*(10**len(str(n+7))+1)+7 # Chai Wah Wu, Jun 29 2025

A032650 Lucky numbers that are concatenations of a number k with itself.

Original entry on oeis.org

33, 99, 2121, 2323, 5151, 5959, 6363, 7171, 7575, 8787, 8989, 9999, 105105, 111111, 117117, 123123, 129129, 135135, 143143, 147147, 153153, 171171, 173173, 177177, 191191, 201201, 237237, 243243, 255255, 263263, 285285, 305305, 309309, 317317

Offset: 1

Patrick De Geest, May 15 1998

Kevin P. Thompson, Table of n, a(n) for n = 1..4215 (first 95 terms from Amiram Eldar)

Intersection of A000959 and A020338.

Cf. A032640.

a(n) = A032640(n) || A032640(n), where || denotes concatenation. - Kevin P. Thompson, Nov 09 2021

More terms from Sascha Kurz, Mar 24 2002

Edited by Charles R Greathouse IV, Apr 26 2010

A077431 n repeated in decimal representation, but separated by enough zeros that the square has the pattern (n^2)(2n^2)(n^2).

Original entry on oeis.org

11, 22, 303, 404, 505, 606, 707, 8008, 9009, 10010, 11011, 12012, 13013, 14014, 15015, 16016, 17017, 18018, 19019, 20020, 21021, 22022, 230023, 240024, 250025, 260026, 270027, 280028, 290029, 300030, 310031, 320032, 330033, 340034, 350035

Offset: 1

Reinhard Zumkeller, Nov 05 2002

A077433(n) = number of separating zeros.

			a(17) = 17017, as 17017^2 = 289578289 = A077432(17) = 289'578'289 and 289=17^2 and 578=2*289.

Cf. A020338, A004216, A077430.

a[n_] := For[idn = IntegerDigits[n]; k = 0, True, k++, an = FromDigits[ Join[idn, Table[0, k], idn]]; If[MatchQ[IntegerDigits[an^2], {b__ /; IntegerQ[Sqrt[FromDigits[{b}]]], c___, 0..., b__} /; FromDigits[{c}] == 2*FromDigits[{b}]], Return[an]]];
Array[a, 35] (* Jean-François Alcover, Nov 13 2017 *)

a(n) = n*(1+10^(1+floor(log_10(2*n^2)))).

A084855 Triangular array, read by rows: T(n,k) = concatenated decimal representations of k and n, 1<=k<=n.

Original entry on oeis.org

11, 12, 22, 13, 23, 33, 14, 24, 34, 44, 15, 25, 35, 45, 55, 16, 26, 36, 46, 56, 66, 17, 27, 37, 47, 57, 67, 77, 18, 28, 38, 48, 58, 68, 78, 88, 19, 29, 39, 49, 59, 69, 79, 89, 99, 110, 210, 310, 410, 510, 610, 710, 810, 910, 1010, 111, 211, 311, 411, 511, 611, 711, 811, 911, 1011, 1111

Offset: 1

Reinhard Zumkeller, Jun 09 2003

Indranil Ghosh, Rows 1..100 of triangle, flattened

Cf. A020338, A055642, A066686, A067574, A084854, A349520.

def T(n, k): return int(str(k) + str(n))
def auptorow(maxrow):
    return [T(n, k) for n in range(1, maxrow+1) for k in range(1, n+1)]
print(auptorow(11)) # Michael S. Branicky, Nov 21 2021

T(n, k) = k*10^A055642(n) + n.

T(n, n) = A020338(n).

A175605 a(n) = concatenation of n^3 with itself.

Original entry on oeis.org

11, 88, 2727, 6464, 125125, 216216, 343343, 512512, 729729, 10001000, 13311331, 17281728, 21972197, 27442744, 33753375, 40964096, 49134913, 58325832, 68596859, 80008000, 92619261, 1064810648, 1216712167, 1382413824, 1562515625

Offset: 1

Vincenzo Librandi, Nov 15 2010

			Concatenation 1 and 1=11; 8 and 8=88; 27 and 27=2727; etc.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A020338.

[Seqint(Intseq(n^3) cat Intseq(n^3)): n in [1..40]]; // Vincenzo Librandi, Jan 01 2015

Table[FromDigits[Join[IntegerDigits[n^3], IntegerDigits[n^3]]], {n, 40}] (* Vincenzo Librandi, Jan 01 2015 *)

A206527 3^n concatenated with itself.

Original entry on oeis.org

11, 33, 99, 2727, 8181, 243243, 729729, 21872187, 65616561, 1968319683, 5904959049, 177147177147, 531441531441, 15943231594323, 47829694782969, 1434890714348907, 4304672143046721, 129140163129140163, 387420489387420489

Offset: 0

Vincenzo Librandi, Mar 14 2012

			a(1)=33 because 3^1 concatenated with 3^1 is 33.

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Cf. A178664, A000244.

[Seqint(Intseq(3^n) cat Intseq(3^n)): n in [0..18]]; // Bruno Berselli, Mar 14 2012

Table[FromDigits[Join[IntegerDigits[3^n], IntegerDigits[3^n]]], {n, 0, 18}] (* Bruno Berselli, Mar 14 2012 *)
Table[3^n 10^IntegerLength[3^n]+3^n,{n,0,20}] (* Harvey P. Dale, May 27 2019 *)

a(n) = A020338(3^n). - Bruno Berselli, Mar 14 2012

A248422 Even integers concatenated with themselves.

Original entry on oeis.org

22, 44, 66, 88, 1010, 1212, 1414, 1616, 1818, 2020, 2222, 2424, 2626, 2828, 3030, 3232, 3434, 3636, 3838, 4040, 4242, 4444, 4646, 4848, 5050, 5252, 5454, 5656, 5858, 6060, 6262, 6464, 6666, 6868, 7070, 7272, 7474, 7676, 7878, 8080, 8282, 8484, 8686, 8888, 9090, 9292, 9494, 9696, 9898, 100100

Offset: 1

Lev Krasnovsky, Oct 06 2014

Bisection of A020338.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A020338.

[Seqint(Intseq(n) cat Intseq(n)): n in [2..100 by 2]]; // Vincenzo Librandi, Oct 21 2014

FromDigits[Flatten[IntegerDigits/@#]]&/@Partition[With[{c=2*Range[ 50]}, Riffle[c,c]],2] (* or *) Table[n*10^IntegerLength[n]+n,{n,2,100,2}] (* Harvey P. Dale, Jun 11 2019 *)

a(n) = eval(concat(Str(2*n), Str(2*n))); \\ Michel Marcus, Oct 06 2014

a(n) = 2*n*10^ceiling(log_10(2*n)) + 2*n. - Tom Edgar, Oct 21 2014

cp's OEIS Frontend

A116160 Numbers k such that k concatenated with itself gives the product of two numbers which differ by 7.

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A178664 a(n) = 2^n concatenated with itself.

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A032610 Concatenation of n and n + 5 or {n,n+5}.

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A032612 Concatenation of n and n+7.

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A032650 Lucky numbers that are concatenations of a number k with itself.

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A077431 n repeated in decimal representation, but separated by enough zeros that the square has the pattern (n^2)(2n^2)(n^2).

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A084855 Triangular array, read by rows: T(n,k) = concatenated decimal representations of k and n, 1<=k<=n.

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Python

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A175605 a(n) = concatenation of n^3 with itself.

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Magma

Mathematica

A206527 3^n concatenated with itself.

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Magma

Mathematica

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A248422 Even integers concatenated with themselves.