A058413 -id:A058413 - 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

A058414 Squares composed of digits {0,1,4}, not ending with zero.

Original entry on oeis.org

1, 4, 144, 441, 1444, 10404, 40401, 1004004, 1100401, 4004001, 100040004, 114041041, 400040001, 414041104, 10000400004, 10110101401, 40000400001, 41011110144, 141001001001, 414441100441, 1000004000004, 1041110041104, 4000004000001, 4011400111104, 100000040000004

Offset: 1

Patrick De Geest, Nov 15 2000

Patrick De Geest, Index to related sequences.
Hisanori Mishima, Sporadic tridigital solutions.

Cf. A058413.

a(n) = A058413(n)^2. - Elmo R. Oliveira, Jul 18 2025

More terms added using A058413 by Elmo R. Oliveira, Jul 18 2025

A378048 Numbers k such that k and k^2 together use at most 4 distinct decimal digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 19, 20, 21, 22, 23, 25, 26, 27, 28, 30, 31, 35, 38, 40, 41, 45, 46, 50, 55, 56, 60, 63, 64, 65, 66, 68, 70, 74, 75, 76, 77, 80, 81, 83, 85, 88, 90, 91, 95, 96, 97, 99, 100, 101, 102, 105, 109, 110

Offset: 1

Jovan Radenkovicc, Nov 15 2024

Problem: Is there a real constant c such that a(n) < n^c for all positive integers n?

All of A136808, A136809, A136816, ..., A137079 are subsequences. Many if not most terms of A058411, A058413, ... ("tridigital solutions") are also in this sequence; see also Hisanori Mishima's web page for some nontrivial solutions. - M. F. Hasler, Feb 02 2025

			816 is in the sequence since 816^2 = 665856 and both together use at most 4 distinct digits.
149 is not in the sequence since 149^2 = 22201 and both together use 5 distinct digits.

Daniel Mondot, Table of n, a(n) for n = 1..10000 (first 748 terms from Jovan Radenkovicc)
M. F. Hasler, Numbers avoiding certain digits, OEIS wiki, Jan 12 2020
Hisanori Mishima, Sporadic tridigital solutions
OEIS index for squares having only given digits

Supersequence of A136808, A136809, A136816, A136822.

Cf. A043537, A053061, A055436, A154155.

[n: n in [0..1000000] | #Set(Intseq(n)) le 4 and #Set(Intseq(n) cat Intseq(n^2)) le 4];

Select[Range[0, 110], Length[Union @@ IntegerDigits@ {#, #^2}] < 5 &] (* Amiram Eldar, Nov 15 2024 *)

isok(k) = #Set(concat(digits(k), digits(k^2))) <= 4; \\ Michel Marcus, Nov 15 2024

is(n)=my(s=Set(digits(n))); #s<5 && #setunion(Set(digits(n^2)),s)<5 \\ Charles R Greathouse IV, Jan 30 2025

is1(n)=#setunion(Set(digits(n^2)),Set(digits(n)))<5
ok(m)=my(d=concat(apply(k->digits(lift(k)), [m,m^2]))
test(d)=my(v=List(),D=10^d); for(n=0,D-1, if(ok(Mod(n,D)), listput(v,n))); Vec(v)
res=test(8); \\ build a list of residues mod 10^8
D=diff(concat(res,res[1]+10^8)); #D
u=List(); for(n=0,10^7, if(is1(n) && !setsearch(n,res), listput(u,n))); \\ build exceptions
setminus(select(is1,[0..n]),list(n))
list(lim)=my(v=List(u)); forstep(n=0,lim,D, if(is1(n), listput(v,n))); Vec(v) \\ Charles R Greathouse IV, Jan 30 2025

def ok(n): return len(set(str(n)+str(n**2))) <= 4
print([k for k in range(111) if ok(k)]) # Michael S. Branicky, Nov 18 2024

A043537(A053061(a(n))) <= 4.

Trivially, a(n) >> n^1.66... where the exponent is log(10)/log(4) (A154155). - Charles R Greathouse IV, Jan 30 2025

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

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A058414 Squares composed of digits {0,1,4}, not ending with zero.

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A378048 Numbers k such that k and k^2 together use at most 4 distinct decimal digits.

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