A277946 -id:A277946 - cp's OEIS frontend

A277959 Numbers k such that 2 is the largest decimal digit of k^2.

11, 101, 110, 149, 1001, 1010, 1011, 1100, 1101, 1490, 10001, 10010, 10011, 10100, 10110, 11000, 11001, 11010, 14499, 14900, 100001, 100010, 100011, 100100, 100101, 100110, 101000, 101001, 101100, 110000, 110001, 110010, 110100, 144990, 149000, 316261

Offset: 1

Colin Barker, Nov 06 2016

The terms > 1 of A058411 can be considered as primitive elements of this sequence, obtained by multiplying those by powers of 10 (cf. formula). These terms of A058411 have at least 2 nonzero digits, and therefore their square has at least one digit 2. - M. F. Hasler, Nov 15 2017

M. F. Hasler, Table of n, a(n) for n = 1..1380 (first 50 terms from Colin Barker)
OEIS Index to sequences related to squares.

Cf. A277946 (the squares); A277960, A277961, A295005, ..., A295009 (analog for largest digit 3, 4, 5, ..., 9).
Cf. A058411, A058412 and A058413, ..., A058474. (Similar but no trailing 0's allowed.)
Cf. A136808 and A136809, ..., A137147 for other digit combinations. (Numbers must satisfy the same restriction as their squares.)

Select[Range[4*10^5], And[#[[2]] > 0, Union@ Take[RotateLeft[#, 2], 7] == {0}] &@ DigitCount[#^2] &] (* Michael De Vlieger, Nov 16 2017 *)

L=List(); for(n=1, 10000, if(vecmax(digits(n^2))==2, listput(L, n))); Vec(L)

A277959(LIM=1e15, L=List(), N=1)={while(LIM>N=next_A058411(N),my(t=N); until(LIMM. F. Hasler, Nov 15 2017

Equals (A058411 \ {1})*A011557, where A011557 = { 10^k; k >= 0 }. - M. F. Hasler, Nov 16 2017

Edited by M. F. Hasler, Nov 16 2017

A136808 Numbers k such that k and k^2 use only the digits 0, 1 and 2.

Original entry on oeis.org

0, 1, 10, 11, 100, 101, 110, 1000, 1001, 1010, 1011, 1100, 1101, 10000, 10001, 10010, 10011, 10100, 10110, 11000, 11001, 11010, 100000, 100001, 100010, 100011, 100100, 100101, 100110, 101000, 101001, 101100, 110000, 110001, 110010, 110100, 1000000, 1000001, 1000010, 1000011, 1000100

Offset: 1

Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008

Generated with DrScheme.
Subsequence of A136809, A136816, ..., A136836. - M. F. Hasler, Jan 24 2008
A278038(18) = 10101, A136827(294) = 10110001101, A136831(1276) = 101100010001101 resp. A136836(1262) = 101090009991101 are the first terms from where on these four sequences differ from the present one. - M. F. Hasler, Nov 15 2017
From Jovan Radenkovicc, Nov 15 2024: (Start)
A nonnegative integer n is in this sequence iff 10*n is also in this sequence.
Not a subsequence of A278038 (binary numbers without '111'). A counterexample is 10^2884 + 10^2880 + 10^2872 + 10^2857 + 10^2497 + 10^2426 + 10^2285 + 10^2004 + 10^1443 + 10^1442 + 10^1441 + 10^881 + 10^600 + 10^459 + 10^388 + 10^27 + 10^12 + 10^4 + 1. There are infinitely many counterexamples not divisible by 10. This counterexample follows from the fact that 111^2+2000*4+200*4=12321+8000+800=21121. In fact, every binary substring will eventually occur in this sequence. Also, if n is a term containing only the digits 0 and 1, then 10^k*n+1 and n+10^k are also in this sequence for any sufficiently large integer k. (End)

			101000100100001^2 = 10201020220210222010200200001.

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1359 terms from Jonathan Wellons)
Jonathan Wellons, Tables of Shared Digits [archived]
Index to sequences related to squares.

A subsequence of the binary numbers A007088.
Cf. A278038.
Cf. A136809, A136810, ..., A137147 for other digit combinations.
See also A058412 = A058411^2: squares having only digits {0,1,2}, A277946 = A277959^2 = squares whose largest digit is 2.

isA136808 := proc(n) local ndgs,n2dgs ; ndgs := convert(convert(n,base,10),set) ; n2dgs := convert(convert(n^2,base,10),set) ; if ( (ndgs union n2dgs) minus {0,1,2} ) = {} then true ; else false ; fi ; end: LtonRev := proc(L) local i ; add(op(i,L)*10^(i-1),i=1..nops(L)) ; end: A007089 := proc(n) convert(n,base,3) ; LtonRev(%) ; end: n := 1: for i from 0 do n3 := A007089(i) ; if isA136808(n3) then printf("%d %d ",n,n3) ; n := n+1 ; fi ; od: # R. J. Mathar, Jan 24 2008

Select[FromDigits/@Tuples[{0,1},7],Union[Take[DigitCount[#^2],{3,9}]]=={0}&] (* Harvey P. Dale, May 29 2013 *)

for(n=1,999,vecmax(digits((N=fromdigits(binary(n),10))^2))<3 && print1(N",")) \\ M. F. Hasler, Nov 15 2017

A277948 Squares whose largest decimal digit is 4.

Original entry on oeis.org

4, 144, 324, 400, 441, 1024, 1444, 2304, 2401, 10404, 14400, 23104, 32041, 32400, 33124, 40000, 40401, 44100, 101124, 102400, 103041, 110224, 114244, 121104, 131044, 144400, 203401, 204304, 213444, 230400, 232324, 240100, 300304, 301401, 421201, 1004004

Offset: 1

Colin Barker, Nov 05 2016

A subsequence of A158082, in turn a subsequence of A000290.

Colin Barker, Table of n, a(n) for n = 1..1000

Cf. A000290 (the squares).
Cf. A277961 (square roots of these terms).
Cf. A277946, A277947, A295015, ..., A295019 (analog for largest digit = 2, 3, 5, ..., 9).
Cf. A058412, A058411, ..., A058474 and A136808, A136809, ..., A137147 for other restrictions on digits of squares.

[n^2: n in [1..1000000] | Maximum(Intseq(n^2)) eq 4]; // Vincenzo Librandi, Nov 06 2016

Select[Range[1100]^2,Max[IntegerDigits[#]]==4&] (* Harvey P. Dale, Jul 01 2017 *)

L=List(); for(n=1, 10000, if(vecmax(digits(n^2))==4, listput(L, n^2))); Vec(L)

a(n) = A277961(n)^2. - M. F. Hasler, Nov 12 2017

Intersection of A000290 and A277966. - M. F. Hasler, Nov 15 2017

A030175 When squared gives number composed of digits {1,2,3}.

Original entry on oeis.org

1, 11, 111, 36361, 363639, 461761, 3636361, 34815389, 362397739, 176412364139, 57637950363639, 3497458093147239, 56843832676142723489, 557963558954625926861

Offset: 1

Patrick De Geest

P. De Geest, Squares containing at most three distinct digits, Index entries for related sequences
Author?, Source(txt)
Hisanori Mishima, Sporadic tridigital solutions
Eric Weisstein's World of Mathematics, Square Number.
Index entries for sequences related to squares.

Cf. A030174; A000290.
Cf. A006716 = A027675^2, A030176 = A030177^2, A058411^2 = A058412, ..., A058473^2 = A058474.
Cf. A136808, A136809, ..., A137147: n and n^2 have digits {...}.
Cf. A277959^2 = A277946 and A277960^2 = A277947: squares whose largest digit is 2 resp. 3.

Do[ If[ Union[ Join[{1, 2, 3}, IntegerDigits[n^2] ] ] == {1, 2, 3}, Print[n] ], {n, 0, 10^9}]

lista(nn) = for(n=1, nn, if(setminus(vecsort(digits(n^2), , 8), [1, 2, 3])==[], print1(n, ", "))) \\ Iain Fox, Nov 16 2017

a(n)^2 = A030174(n). - M. F. Hasler, Nov 16 2017

More terms from Patrick De Geest, Mar 01 2000
More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 14 2005
Offset corrected by Iain Fox, Nov 16 2017

A058412 Squares composed of digits {0,1,2}, not ending with zero.

Original entry on oeis.org

1, 121, 10201, 22201, 1002001, 1022121, 1212201, 100020001, 100220121, 121022001, 210221001, 10000200001, 10002200121, 10020210201, 10201202001, 12100220001, 100021020121, 1000002000001, 1000022000121, 1000202010201

Offset: 1

Patrick De Geest, Nov 15 2000

All terms but the first one have their largest digit equal to 2, cf. A277946 = A277959^2. - M. F. Hasler, Nov 15 2017

P. De Geest, Index to related sequences
Hisanori Mishima, Sporadic tridigital solutions
OEIS Index to sequences related to squares.

Cf. A058411.
Cf. A063009, A066139. - Zak Seidov, Jul 01 2013
Cf. A136808, A136809 and A136810, ..., A137147 for other digit combinations.
See also A277946 = A277959^2 = squares whose largest digit is 2.
The first 1261 terms are also a subsequence of A278038 (binary numbers without '111'), in turn a subsequence of the binary numbers A007088.

apply( t->t^2, vector(100,i,N=if(i>1,next_A058411(N),1))) \\ M. F. Hasler, Nov 15 2017

a(n) = A058411(n)^2. - Zak Seidov, Jul 01 2013

A277947 Squares whose largest decimal digit is 3.

Original entry on oeis.org

12321, 123201, 130321, 1232100, 1320201, 3101121, 12320100, 13032100, 102030201, 102232321, 103002201, 123210000, 123232201, 132020100, 310112100, 1232010000, 1303210000, 1322122321, 1332323001, 2103231321, 10022212321, 10130221201, 10203020100, 10203222121

Offset: 1

Colin Barker, Nov 05 2016

A subsequence of A000290.

Colin Barker, Table of n, a(n) for n = 1..100

Cf. A000290.

Cf. A277946, A277948, A277960.

[n^2: n in [1..1000000] | Maximum(Intseq(n^2)) eq 3]; // Vincenzo Librandi, Nov 06 2016

L=List(); for(n=1, 10000, if(vecmax(digits(n^2))==3, listput(L, n^2))); Vec(L)

A295015 Squares whose largest digit is 5.

Original entry on oeis.org

25, 225, 1225, 1521, 2025, 2500, 3025, 4225, 5041, 11025, 12544, 13225, 21025, 22500, 24025, 34225, 35344, 42025, 44521, 52441, 55225, 112225, 122500, 133225, 135424, 150544, 151321, 152100, 202500, 212521, 235225, 245025, 250000, 251001, 252004, 255025, 302500

Offset: 1

M. F. Hasler, Nov 12 2017

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A295015 (square roots of the terms); A277946, A277947, A277948, A295016 .. A295019 (analog for digits 2 through 9); A295025 (analog for cubes).

Cf. A000290 (the squares).

Select[Range[600]^2,Max[IntegerDigits[#]]==5&] (* Harvey P. Dale, Aug 19 2022 *)

is_A295015(n)=issquare(n)&&n&&vecmax(digits(n))==5 \\ The "n&&" avoids an error message for n = 0.

from math import isqrt
def aupto(limit):
  alst, rootlimit = [], isqrt(limit)
  for k in range(1, rootlimit+1):
    if max(str(k*k)) == "5": alst.append(k*k)
  return alst
print(aupto(302500)) # Michael S. Branicky, May 15 2021

a(n) = A295005(n)^2.

A295019 Squares whose largest digit is 9.

Original entry on oeis.org

9, 49, 169, 196, 289, 529, 729, 900, 961, 1089, 1296, 1369, 1849, 1936, 2209, 2809, 2916, 3249, 3969, 4096, 4489, 4900, 5329, 5929, 6889, 7396, 7569, 7921, 8649, 9025, 9216, 9409, 9604, 9801, 10609, 11449, 12769, 12996, 13689, 13924, 15129, 16129, 16900, 17689, 17956, 18496, 18769

Offset: 1

M. F. Hasler, Nov 12 2017

Cf. A295009 (square roots of the terms), A277946 - A277948 (same for digit 2..4), A295015 - A295018 (same for digit 5..8).

Cf. A000290 (the squares).

Select[Range[150]^2,Max[IntegerDigits[#]]==9&] (* Harvey P. Dale, Oct 27 2019 *)

is_A295019(n)=issquare(n)&&n&&vecmax(digits(n))==9 \\ "&&n" avoids an error message for n=0.

a(n) = A295009(n)^2.

A295016 Squares whose largest digit is 6.

Original entry on oeis.org

16, 36, 64, 256, 361, 625, 1156, 1600, 2116, 2601, 3136, 3364, 3600, 4356, 4624, 5625, 6241, 6400, 6561, 11236, 11664, 13456, 14161, 14641, 15625, 16641, 20164, 21316, 24336, 25600, 26244, 30625, 36100, 41616, 42436, 43264, 46225, 46656, 50625, 53361, 56644, 60025, 60516, 61504

Offset: 1

M. F. Hasler, Nov 12 2017

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

Cf. A295006 (square roots of the terms); A277946, A277947, A277948, A295015 .. A295019 (analog for digits 2 through 9), A295021 (analog for cubes).

Cf. A000290 (the squares).

Select[Range[250]^2,Max[IntegerDigits[#]]==6&] (* Harvey P. Dale, Jun 14 2025 *)

is_A295016(n)=issquare(n)&&n&&vecmax(digits(n))==6 \\ The "n&&" avoids an error message for n = 0.

a(n) = A295006(n)^2.

A295018 Squares whose largest digit is 8.

Original entry on oeis.org

81, 484, 784, 841, 1681, 3481, 3844, 5184, 6084, 8100, 8281, 8464, 8836, 10816, 11881, 14884, 15876, 16384, 18225, 22801, 25281, 28224, 28561, 31684, 33856, 36481, 36864, 38025, 38416, 40804, 43681, 48400, 48841, 53824, 58081, 58564, 67081, 68121, 68644, 71824, 77284, 77841, 78400

Offset: 1

M. F. Hasler, Nov 12 2017

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A295008 (square roots of the terms), A277946 - A277948 (same for digit 2..4), A295015 - A295019 (same for digit 5..9).

Cf. A000290 (the squares).

Res:= NULL: count:= 0:
for n from 1 while count < 50 do
  if max(convert(n^2,base,10))=8 then
    count:= count+1; Res:= Res, n^2;
  fi
od:
Res; # Robert Israel, Jul 21 2019

Select[Range[300]^2,Max[IntegerDigits[#]]==8&] (* Harvey P. Dale, Jul 08 2020 *)

is_A295018(n)=issquare(n)&&n&&vecmax(digits(n))==8 \\ "&&n" avoids an error message for n=0.

a(n) = A295008(n)^2.

cp's OEIS Frontend

A277959 Numbers k such that 2 is the largest decimal digit of k^2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

PARI

Formula

Extensions

A136808 Numbers k such that k and k^2 use only the digits 0, 1 and 2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

A277948 Squares whose largest decimal digit is 4.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A030175 When squared gives number composed of digits {1,2,3}.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A058412 Squares composed of digits {0,1,2}, not ending with zero.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Formula

A277947 Squares whose largest decimal digit is 3.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

PARI

A295015 Squares whose largest digit is 5.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Python

Formula