A277960 -id:A277960 - 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

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

A278937 Numbers k such that 3 is the largest decimal digit of k^3.

Original entry on oeis.org

11, 101, 110, 1001, 1010, 1100, 10001, 10010, 10100, 11000, 100001, 100010, 100100, 101000, 110000, 684917, 1000001, 1000010, 1000100, 1001000, 1010000, 1100000, 6849170, 10000001, 10000010, 10000100, 10001000, 10010000, 10100000, 11000000

Offset: 1

Colin Barker, Dec 02 2016

A038444 is a subsequence. Are there an infinite number of terms not in A038444 that are not a multiple of 10? - Chai Wah Wu, Dec 02 2016
Conjecture: sequence is equal to A038444 plus terms of the form 684917*10^k for k >= 0. - Chai Wah Wu, Sep 02 2017
Conjecture is true up to 4.8*10^18. - Giovanni Resta, Sep 03 2017

			684917 is in the sequence because 684917^3 = 321302302131323213.

Chai Wah Wu, Table of n, a(n) for n = 1..130

Cf. A000578 (the cubes: n^3), A038444, A277960 (analog for squares), A278936 (cubes of the terms: a(n)^3).

Cf. A031997 (the odd terms).

[n: n in [1..2*10^7] | Max(Intseq(n^3)) eq 3]; // Vincenzo Librandi, Dec 03 2016

Select[Range[11 10^6],Max[IntegerDigits[#^3]]==3&] (* Harvey P. Dale, Feb 11 2025 *)

select(n->vecmax(digits(n^3))==3, vector(1000000, n, n))

a(n)^3 = A278936(n).

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)

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.

A137146 Numbers k such that k and k^2 use only the digits 5, 6, 7 and 8.

Original entry on oeis.org

76, 766, 7666, 76666, 766666, 7666666, 76666666, 766666666, 7666666666, 76666666666, 766666666666, 7666666666666, 76666666666666, 766666666666666, 7666666666666666, 76666666666666666, 766666666666666666, 7666666666666666666, 76666666666666666666, 766666666666666666666

Offset: 1

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

Generated with DrScheme.

The first digit of each term is either 7 or 8 and the last digit is 6. - Chai Wah Wu, May 25 2021

			766666666666666^2 = 587777777777776755555555555556.

Jonathan Wellons, Tables of Shared Digits [archived].
OEIS Index to sequences related to squares.

Cf. A000290 (the squares); A136808, A136809, ..., A137147 for other digit combinations.
Cf. A058469 - A058472 and A058411, ..., A058474 for other digit combinations.
Cf. A277959, A277960, A277961, A295005, ..., A295009 (squares with largest digit = 2, 3, 4, 5, ..., 9).

from itertools import product
A137146_list = [n for n in (int(''.join(d)) for l in range(1,6) for d in product('5678',repeat=l)) if set(str(n**2)) <= set('5678')] # Chai Wah Wu, May 25 2021

a(15)-a(20) from Pontus von Brömssen, Apr 12 2024

cp's OEIS Frontend

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

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

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

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

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A278937 Numbers k such that 3 is the largest decimal digit of k^3.

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A277947 Squares whose largest decimal digit is 3.

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Magma

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

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A137146 Numbers k such that k and k^2 use only the digits 5, 6, 7 and 8.

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