A277959 -id:A277959 - cp's OEIS frontend

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

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

A277946 Squares whose largest decimal digit is 2.

Original entry on oeis.org

121, 10201, 12100, 22201, 1002001, 1020100, 1022121, 1210000, 1212201, 2220100, 100020001, 100200100, 100220121, 102010000, 102212100, 121000000, 121022001, 121220100, 210221001, 222010000, 10000200001, 10002000100, 10002200121, 10020010000, 10020210201

Offset: 1

Colin Barker, Nov 05 2016

A subsequence of A000290.
From Robert Israel, Nov 14 2016: (Start)
If n is a term, then so is 100*n.
The first term with an even number of digits is a(36) = 100021020121.
The first term with an even number of digits that is not of the form a(36)*100^k has at least 24 digits.
(End)

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms n = 1..50 from Colin Barker, terms n = 51..474 from Robert Israel)

Cf. A000290, A277947, A277948, A277959.

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

res:= NULL: B:= [1,2]:
for m from 1 to 10 do
  for q in B do
    for x from ceil(sqrt(10^m*q)) to floor(sqrt(10^m*q + 2/9*(10^m-1))) do
      if max(convert(x^2,base,10)) = 2 then res:= res, x^2 fi
  od od:
  for q in B do
     for x from ceil(sqrt(10^(m+1)*q)) to floor(sqrt(10^(m+1)*q + 2/9*(10^(m+1)-1))) do
       if max(convert(x^2,base,10)) = 2 then res:= res, x^2 fi
  od od:
  if m < 10 then B:= map(t -> (10*t,10*t+1,10*t+2),B) fi;
od:
res; # Robert Israel, Nov 14 2016

fQ[n_] := Union[ IntegerDigits[ n^2]][[-1]] == 2; Select[ Range@100500, fQ]^2 (* Robert G. Wilson v, Nov 06 2016 *)

L=List(); for(n=1, 10000, if(vecmax(digits(n^2))==2, listput(L, n^2))); Vec(L)
\\ See A277959 for more efficient code. - M. F. Hasler, Nov 16 2017

a(n) = A277959(n)^2. Intersection of A000290 and A277964. - M. F. Hasler, Nov 15 2017

A277961 Numbers n such that 4 is the largest decimal digit of n^2.

Original entry on oeis.org

2, 12, 18, 20, 21, 32, 38, 48, 49, 102, 120, 152, 179, 180, 182, 200, 201, 210, 318, 320, 321, 332, 338, 348, 362, 380, 451, 452, 462, 480, 482, 490, 548, 549, 649, 1002, 1012, 1020, 1021, 1049, 1102, 1111, 1188, 1200, 1201, 1429, 1488, 1498, 1518, 1520

Offset: 1

Colin Barker, Nov 06 2016

The actual squares are listed in A277948. - M. F. Hasler, Nov 12 2017
Includes 2*10^n+10^m for all n <> m. - Robert Israel, Nov 13 2017
For any term of q digits, the first m digits don't exceed (2 * 10^m - 2) / 3 = 666..66 (m 6's) for 1 <= m <= q. - David A. Corneth, Nov 13 2017
A term a(n) is in the sequence if and only if a(n)*10^k is in the sequence, for all k >= 0. If a(n) = (x*10^k + y)*10^m with 2xy < 10^k, then (y*10^k+x)*10^m' is also in the sequence, for all m'. - M. F. Hasler, Nov 13 2017

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

Cf. A277948, A277959, A277960.

select(n -> max(convert(n^2,base,10))=4, [$1..10000]); # Robert Israel, Nov 13 2017

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

a(n) = sqrt(A277948(n)), where sqrt = A000196 or A000194 or A003059. - M. F. Hasler, Nov 12 2017

A137147 Numbers k such that k and k^2 use only the digits 5, 6, 7, 8 and 9.

Original entry on oeis.org

76, 87, 766, 887, 7666, 8887, 9786, 76587, 76666, 87576, 759576, 766666, 869866, 869867, 886886, 888587, 988866, 7666666, 8766867, 8885887, 76587576, 76666666, 76789686, 86998666, 87565786, 87685676, 88766867, 97759786, 97957576, 766666666, 875765766, 886885887, 887579686, 977699687

Offset: 1

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

Generated with DrScheme.

			989878759589576^2 = 979859958686597599779967859776.

Jonathan Wellons, Table of n, a(n) for n = 1..183
J. Wellons, Tables of Shared Digits [archived]
OEIS Index to sequences related to squares.

Cf. A136808, A136809, ..., A137146 for other digit combinations.
Cf. A000290 (the squares); A027675, A058411, ..., A058474 (3-digit combinations).
Cf. A277959, A277960, A277961, A295005, ..., A295009 (squares with largest digit = 2, 3, 4, 5, ..., 9).

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

A277960 Numbers n such that 3 is the largest decimal digit of n^2.

Original entry on oeis.org

111, 351, 361, 1110, 1149, 1761, 3510, 3610, 10101, 10111, 10149, 11100, 11101, 11490, 17610, 35100, 36100, 36361, 36501, 45861, 100111, 100649, 101010, 101011, 101110, 101149, 101490, 110101, 111000, 111001, 111010, 114111, 114499, 114900, 176100, 176361

Offset: 1

Colin Barker, Nov 06 2016

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

Cf. A277947, A277959, A277961.

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

A295005 Numbers n such that the largest digit of n^2 is 5.

Original entry on oeis.org

5, 15, 35, 39, 45, 50, 55, 65, 71, 105, 112, 115, 145, 150, 155, 185, 188, 205, 211, 229, 235, 335, 350, 365, 368, 388, 389, 390, 450, 461, 485, 495, 500, 501, 502, 505, 550, 579, 585, 595, 635, 650, 652, 665, 671, 710, 711, 715, 718, 729, 735, 745, 1005, 1015, 1050

Offset: 1

M. F. Hasler, Nov 12 2017

			39 is in this sequence because 39^2 = 1521 has 5 as largest digit.

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

Cf. A295015 (the corresponding squares), A277959 .. A277961 (same for digit 2 .. 4), A295006 .. A295009 (same for digit 6 .. 9).

Cf. A000290 (the squares).

Select[Sqrt[ #]&/@(FromDigits/@Select[Tuples[ Range[ 0,5],7],Max[#] == 5&]),IntegerQ] (* Harvey P. Dale, Sep 23 2021 *)

select( is_A295005(n)=n&&vecmax(digits(n^2))==5 , [0..999]) \\ The "n&&" avoids an error message for n=0.

def aupto(limit):
  alst = []
  for k in range(1, limit+1):
    if max(str(k*k)) == "5": alst.append(k)
  return alst
print(aupto(1050)) # Michael S. Branicky, May 15 2021

a(n) = sqrt(A295015(n)), where sqrt = A000196 or A000194 or A003059.

A295009 Numbers k such that the largest digit of k^2 is 9.

Original entry on oeis.org

3, 7, 13, 14, 17, 23, 27, 30, 31, 33, 36, 37, 43, 44, 47, 53, 54, 57, 63, 64, 67, 70, 73, 77, 83, 86, 87, 89, 93, 95, 96, 97, 98, 99, 103, 107, 113, 114, 117, 118, 123, 127, 130, 133, 134, 136, 137, 138, 139, 140, 141, 143, 147, 148, 153, 157, 158, 161, 163, 164, 167, 170, 171

Offset: 1

M. F. Hasler, Nov 12 2017

			23 is in this sequence because 23^2 = 529 has 9 as largest digit.

Cf. A295019 (the corresponding squares), A277959 .. A277961 (same for digit 2 .. 4), A295005 .. A295008 (same for digit 5 .. 8).

Cf. A000290 (the squares).

select( is_A295009(n)=n&&vecmax(digits(n^2))==9 , [0..999]) \\ The "n&&" avoids an error message for n=0.

a(n) = sqrt(A295019(n)), where sqrt = A000196 or A000194 or A003059.

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

A295006 Numbers n such that the largest digit of n^2 is 6.

Original entry on oeis.org

4, 6, 8, 16, 19, 25, 34, 40, 46, 51, 56, 58, 60, 66, 68, 75, 79, 80, 81, 106, 108, 116, 119, 121, 125, 129, 142, 146, 156, 160, 162, 175, 190, 204, 206, 208, 215, 216, 225, 231, 238, 245, 246, 248, 249, 250, 251, 252, 254, 255, 256, 258, 325, 334, 340, 354, 355, 369, 375, 379

Offset: 1

M. F. Hasler, Nov 12 2017

			19 is in this sequence because 19^2 = 361 has 6 as largest digit.

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

Cf. A295016 (the corresponding squares), A277959, A277960, A277961, A295005 .. A295009 (analog for digits 2 through 9), A294996 (analog for cubes).

Cf. A000290 (the squares).

Select[Range[400],Max[IntegerDigits[#^2]]==6&] (* Harvey P. Dale, Mar 30 2024 *)

select( is_A295006(n)=n&&vecmax(digits(n^2))==6 , [0..999]) \\ The "n&&" avoids an error message for n=0.

a(n) = sqrt(A295016(n)), where sqrt = A000196 or A000194 or A003059.

cp's OEIS Frontend

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

A277946 Squares whose largest decimal digit is 2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula

A277961 Numbers n such that 4 is the largest decimal digit of n^2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

PARI

Formula

A137147 Numbers k such that k and k^2 use only the digits 5, 6, 7, 8 and 9.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A277960 Numbers n such that 3 is the largest decimal digit of n^2.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

A295005 Numbers n such that the largest digit of n^2 is 5.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

Formula

A295009 Numbers k such that the largest digit of k^2 is 9.

Views

Author

Keywords