cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

A167741 Primes that become squares when prefixed with an 8.

Original entry on oeis.org

41, 281, 5849, 8209, 11801, 29921, 33569, 51929, 70489, 77969, 128201, 139609, 196769, 219689, 346321, 415801, 450649, 532241, 543929, 602489, 625969, 684809, 743849, 755681, 767521, 922169, 934121, 946081, 958049
Offset: 1

Views

Author

Claudio Meller, Nov 10 2009

Keywords

Comments

Subsequence of primes of A273363. - Michel Marcus, Jun 24 2016

Links

Crossrefs

Cf. A167734, A167735, A167736, A167737, A167738, A167739, A167740.
Cf. A273363.

Programs

  • Mathematica
    Select[Prime[Range[10000]], IntegerQ[Sqrt[FromDigits[Join[{8}, IntegerDigits[#]]]]]&] (* G. C. Greubel, Jun 23 2016 *)
Select[Prime[Range[80000]],IntegerQ[Sqrt[8*10^IntegerLength[#]+#]]&] (* Harvey P. Dale, Jan 29 2023 *)

Extensions

Definition corrected and sequence extended by Michel Marcus, Aug 05 2013

A273357 Numbers n such that the decimal number concat(2,n) is a square.

Original entry on oeis.org

5, 25, 56, 89, 116, 209, 304, 401, 500, 601, 704, 809, 916, 1025, 1316, 1609, 1904, 2201, 2500, 2801, 3104, 3409, 3716, 4025, 4336, 4649, 4964, 5281, 5600, 5921, 6244, 6569, 6896, 7225, 7556, 7889, 8224, 8561, 8900, 9241, 9584, 9929, 10681
Offset: 1

Views

Author

Nathan Fox, Brooke Logan, and N. J. A. Sloane, May 20 2016

Keywords

Comments

Elements are squares of integers in (sqrt(21), sqrt(30)) * sqrt(10)^k without the leading 2 elements for nonnegative k. - David A. Corneth, May 20 2016

Examples

			56 is a member because 256 = 16^2 is a square.
0 is not a member because 20 is not a square.

Links

Crossrefs

Cf. A272671, A273358, A273359, A273360, A273361, A273362, A273363, A273364.

Programs

  • Magma
    [n: n in [1..15000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(2)))]; // Marius A. Burtea, Mar 21 2019
  • Maple
    t1:=[];
for k from 1 to 20000 do
if issqr(k+2*10^length(k)) then t1:=[op(t1), k]; fi;
od;
t1;

A273358 Numbers n such that the decimal number concat(3,n) is a square.

Original entry on oeis.org

6, 24, 61, 136, 249, 364, 481, 600, 721, 844, 969, 1329, 1684, 2041, 2400, 2761, 3124, 3489, 3856, 4225, 4596, 4969, 5344, 5721, 6100, 6481, 6864, 7249, 7636, 8025, 8416, 8809, 9204, 9601, 10249, 11364, 12481, 13600, 14721, 15844, 16969, 18096
Offset: 1

Views

Author

Nathan Fox, Brooke Logan, and N. J. A. Sloane, May 20 2016

Keywords

Comments

Elements are squares of integers in (sqrt(31), sqrt(40)) * sqrt(10)^k without the leading 3 elements for nonnegative k. - David A. Corneth, May 20 2016

Examples

			61 is a member because 361 = 19^2 is a square.
0 is not a member because 30 is not a square.

Links

Crossrefs

Cf. A272671, A273357, A273359, A273360, A273361, A273362, A273363, A273364.

Programs

  • Magma
    [n: n in [1..20000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(3)))]; // Marius A. Burtea, Mar 21 2019
  • Maple
    t1:=[];
for k from 1 to 20000 do
if issqr(k+3*10^length(k)) then t1:=[op(t1), k]; fi;
od;
t1;

A273359 Numbers k such that the decimal number concat(4,k) is a square.

Original entry on oeis.org

9, 41, 84, 225, 356, 489, 624, 761, 900, 1209, 1616, 2025, 2436, 2849, 3264, 3681, 4100, 4521, 4944, 5369, 5796, 6225, 6656, 7089, 7524, 7961, 8400, 8841, 9284, 9729, 10881, 12164, 13449, 14736, 16025, 17316, 18609, 19904, 21201, 22500
Offset: 1

Views

Author

Nathan Fox, Brooke Logan, and N. J. A. Sloane, May 20 2016

Keywords

Comments

Elements are squares of integers in (sqrt(41), sqrt(50)) * sqrt(10)^k without the leading 4 elements for nonnegative k. - David A. Corneth, May 20 2016

Examples

			84 is a member because 484 = 22^2 is a square.
0 is not a member because 40 is not a square.
sqrt(410) < 21 AND 22 < sqrt(500) < 23 so 21^2 = 441 and 22^2 = 484 give 41 and 84 respectively.
64 < sqrt(4100) < 65 AND 70 < sqrt(5000) < 71 so 65^2 = 4225, 66^2 = 4356, ..., 70^2 = 4900 give 225, 356, ..., 900 respectively. - _David A. Corneth_, May 20 2016

Links

Crossrefs

Cf. A272671, A273357, A273358, A273360, A273361, A273362, A273363, A273364.

Programs

  • Magma
    [n: n in [1..50000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(4)))]; // Vincenzo Librandi, Feb 20 2020
  • Maple
    t1:=[];
for k from 1 to 30000 do
if issqr(k+4*10^length(k)) then t1:=[op(t1), k]; fi;
od;
t1;
  • Mathematica
    Select[Range[45000], IntegerQ[Sqrt[4 10^IntegerLength[#] + #]] &] (* Vincenzo Librandi, Feb 20 2020 *)
DeleteCases[(FromDigits[Drop[IntegerDigits[#], 1]]) & /@ Select[Range[3, 500]^2, IntegerDigits[#][[1]] == 4 && IntegerDigits[#][[2]] != 0 &], 0] (* Alonso del Arte, Feb 20 2020 *)
  • PARI
    a(n) = {my(k=1,t=0); while(n>k, n-=k; t++; k=floor(sqrt(50)*sqrt(10^t))- ceil(sqrt(41)*sqrt(10^t))+1);(ceil(sqrt(41)*sqrt(10^t))+n-1)^2%(40*10^t)} \\ David A. Corneth, May 20 2016
  • Scala
    (3 to 500).map(n => n * n).filter(n => n.toString.startsWith("4") && !n.toString.startsWith("40")).map(n => Integer.parseInt(n.toString.substring(1))) // Alonso del Arte, Feb 20 2020

A273360 Numbers n such that the decimal number concat(5,n) is a square.

Original entry on oeis.org

29, 76, 184, 329, 476, 625, 776, 929, 1076, 1529, 1984, 2441, 2900, 3361, 3824, 4289, 4756, 5225, 5696, 6169, 6644, 7121, 7600, 8081, 8564, 9049, 9536, 11225, 12656, 14089, 15524, 16961, 18400, 19841, 21284, 22729, 24176, 25625, 27076
Offset: 1

Views

Author

Nathan Fox, Brooke Logan, and N. J. A. Sloane, May 20 2016

Keywords

Comments

Elements are squares of integers in (sqrt(51), sqrt(60)) * sqrt(10)^k without the leading 5 elements for nonnegative k. - David A. Corneth, May 20 2016

Examples

			76 is a member because 576 = 24^2 is a square.
0 is not a member because 50 is not a square.

Links

Crossrefs

Cf. A272671, A273357, A273358, A273359, A273361, A273362, A273363, A273364.

Programs

  • Magma
    [n: n in [1..10000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(5)))]; // Marius A. Burtea, Mar 21 2019
  • Maple
    t1:=[];
for k from 1 to 50000 do
if issqr(k+5*10^length(k)) then t1:=[op(t1), k]; fi;
od;
t1;
  • Mathematica
    Select[Range[30000],IntegerQ[Sqrt[5*10^IntegerLength[#]+#]]&] (* Harvey P. Dale, Jan 01 2019 *)

A273361 Numbers n such that the decimal number concat(6,n) is a square.

Original entry on oeis.org

4, 25, 76, 241, 400, 561, 724, 889, 1009, 1504, 2001, 2500, 3001, 3504, 4009, 4516, 5025, 5536, 6049, 6564, 7081, 7600, 8121, 8644, 9169, 9696, 11524, 13089, 14656, 16225, 17796, 19369, 20944, 22521, 24100, 25681, 27264, 28849, 30436
Offset: 1

Views

Author

Nathan Fox, Brooke Logan, and N. J. A. Sloane, May 20 2016

Keywords

Comments

Elements are squares of integers in (sqrt(61), sqrt(70)) * sqrt(10)^k without the leading 6 elements for nonnegative k. - David A. Corneth, May 20 2016

Examples

			76 is a member because 676 = 26^2 is a square.
0 is not a member because 60 is not a square.

Links

Crossrefs

Cf. A272671, A273357, A273358, A273359, A273360, A273362, A273363, A273364.

Programs

  • Magma
    [n: n in [1..20000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(6)))]; // Marius A. Burtea, Mar 21 2019
  • Maple
    t1:=[];
for k from 1 to 50000 do
if issqr(k+6*10^length(k)) then t1:=[op(t1), k]; fi;
od;
t1;
  • Mathematica
    Select[Range[31000],IntegerQ[Sqrt[FromDigits[Join[{6}, IntegerDigits[ #]]]]]&] (* Harvey P. Dale, Feb 09 2019 *)

A273362 Numbers n such that the decimal number concat(7,n) is a square.

Original entry on oeis.org

29, 84, 225, 396, 569, 744, 921, 1289, 1824, 2361, 2900, 3441, 3984, 4529, 5076, 5625, 6176, 6729, 7284, 7841, 8400, 8961, 9524, 10649, 12336, 14025, 15716, 17409, 19104, 20801, 22500, 24201, 25904, 27609, 29316, 31025, 32736, 34449
Offset: 1

Views

Author

Nathan Fox, Brooke Logan, and N. J. A. Sloane, May 20 2016

Keywords

Comments

Elements are squares of integers in (sqrt(71), sqrt(80)) * sqrt(10)^k without the leading 7 elements for nonnegative k. - David A. Corneth, May 20 2016

Examples

			84 is a member because 784 = 28^2 is a square.
0 is not a member because 70 is not a square.

Links

Crossrefs

Cf. A272671, A273357, A273358, A273359, A273360, A273361, A273363, A273364.

Programs

  • Magma
    [n: n in [1..20000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(7)))]; // Marius A. Burtea, Mar 21 2019
  • Maple
    t1:=[];
for k from 1 to 50000 do
if issqr(k+7*10^length(k)) then t1:=[op(t1), k]; fi;
od;
t1;
  • Mathematica
    Select[Range[35000],IntegerQ[Sqrt[7*10^IntegerLength[#]+#]]&] (* Harvey P. Dale, Feb 10 2019 *)

A273364 Numbers n such that the decimal number concat(9,n) is a square.

Original entry on oeis.org

61, 216, 409, 604, 801, 1204, 1809, 2416, 3025, 3636, 4249, 4864, 5481, 6100, 6721, 7344, 7969, 8596, 9225, 9856, 10116, 12025, 13936, 15849, 17764, 19681, 21600, 23521, 25444, 27369, 29296, 31225, 33156, 35089, 37024, 38961, 40900, 42841, 44784
Offset: 1

Views

Author

Nathan Fox, Brooke Logan, and N. J. A. Sloane, May 20 2016

Keywords

Comments

Elements are squares of integers in (sqrt(91), 10) * sqrt(10)^k without the leading 9 elements for nonnegative k. - David A. Corneth, May 20 2016

Examples

			61 is a member because 961 = 31^2 is a square.
0 is not a member because 90 is not a square.

Links

Crossrefs

Cf. A272671, A273357, A273358, A273359, A273360, A273361, A273362, A273363.

Programs

  • Magma
    [n: n in [1..50000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(9)))]; // Vincenzo Librandi, Feb 20 2020
  • Maple
    t1:=[];
for k from 1 to 50000 do
if issqr(k+9*10^length(k)) then t1:=[op(t1), k]; fi;
od;
t1;
  • Mathematica
    Select[Range[45000],IntegerQ[Sqrt[9*10^IntegerLength[#]+#]]&] (* Harvey P. Dale, Feb 19 2020 *)
Showing 1-8 of 8 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.