A136904 -id:A136904 - cp's OEIS frontend

A256708 Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 8 as largest digit.

280, 508, 780, 805, 1028, 1078, 1280, 1308, 1680, 1780, 1805, 1840, 2078, 2608, 2680, 2780, 2800, 2801, 2802, 2805, 2840, 2850, 3280, 3580, 3780, 3805, 3808, 3850, 4048, 4078, 4280, 4780, 4804, 4805, 4880, 5008, 5018, 5028, 5048, 5078, 5080, 5084, 5180, 5280

Offset: 1

Felix Fröhlich, Apr 08 2015

Felix Fröhlich, Table of n, a(n) for n = 1..10000

Cf. A136814, A136820, A136825, A136829, A136832, A136840, A136845, A136849, A136904, A256630, A256631, A256633, A256634, A256709.

fQ[n_] := Block[{c = DigitCount@ n}, And[c[[9]] == 0, c[[8]] > 0, c[[10]] > 0]]; Select[Range@ 5280, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, Apr 12 2015 *)
maxdQ[n_]:=Module[{id1=IntegerDigits[n],id2=IntegerDigits[n^2]},Max[ id1] == Max[ id2] == 8&&Min[id1]==Min[id2]==0]; Select[Range[6000],maxdQ] (* Harvey P. Dale, Oct 19 2021 *)

is(n) = vecmin(digits(n))==0 && vecmin(digits(n^2))==0 && vecmax(digits(n))==8 && vecmax(digits(n^2))==8

A030097 Numbers k such that k^2 has only even digits.

Original entry on oeis.org

0, 2, 8, 20, 22, 68, 78, 80, 92, 162, 168, 200, 202, 220, 262, 298, 478, 492, 498, 668, 680, 780, 800, 898, 908, 920, 932, 1422, 1492, 1498, 1620, 1680, 1692, 2000, 2002, 2020, 2022, 2192, 2200, 2202, 2498, 2502, 2578, 2620, 2832, 2878, 2978, 2980, 4502

Offset: 1

Patrick De Geest

A136904 is a subsequence. - Zak Seidov, Dec 03 2012

Zak Seidov, Table of n, a(n) for n = 1..2000

Cf. A030098, A136904.

Select[ Range[ 3000 ], Union[ EvenQ[ IntegerDigits[ #^2 ] ] ] == {True} & ]

is_A030097(n)=!setminus(Set(Vec(Str(n^2))),Vec("02468"))  \\ M. F. Hasler, Dec 13 2011

a(n) = sqrt(A030098(n)). - Zak Seidov, Dec 03 2012

More terms from Zak Seidov, May 24 2010

A385300 Integers k containing only odd digits, except the last digit, such that k^2 is composed of only even digits.

Original entry on oeis.org

2, 8, 78, 92, 932, 7798, 51192, 939398, 5157798, 7797578, 7797978, 9393978, 15119592, 15773398, 53179378, 53559332, 77979998, 79175932, 155139378, 157759592, 517751738, 535393932, 917933998, 939597798, 1511979592, 5157759592, 7771757978, 7775735378, 9393959798

Offset: 1

Gonzalo Martínez, Jun 24 2025

Although the terms in this list contain only odd digits, except for the units digit, their squares have only even digits.
The terms of the list are even numbers ending only in 2 or in 8. Proof: if n ends in 0, 4 or 6, since the penultimate digit of n is odd, then the last 2 digits of n can be: 10, 14, 16, 30, 34, 36, 50, 54, 56, 70, 74, 76, 90, 94 and 96. If n ends in 10, 30, 50, 70 or 90, then the antepenultimate digit of n^2 is odd, while in the other cases the penultimate digit of n^2 is odd.
a(n) == 32, 38, 78, 92, 98 (mod 100), for n > 3.
a(n) == 192, 332, 338, 378, 398, 578, 592, 738, 798, 932, 978, 992, 998 (mod 1000), for n > 4. - Chai Wah Wu, Jun 25 2025

			7798 is a term, since only the last digit is even and 7798^2 = 60808804, whose digits are all even.

David A. Corneth, Table of n, a(n) for n = 1..360
David A. Corneth, PARI program

Cf. A000290, A014261, A030097, A136904.

Select[Range[10^7],NoneTrue[Take[IntegerDigits[#],IntegerLength[#]-1],EvenQ]&&AllTrue[IntegerDigits[#^2],EvenQ]&] (* James C. McMahon, Jun 28 2025 *)

odd(n) = {my(k=1); while(n>5^k, n-=5^k; k++); fromdigits([2*d+1 | d<-digits(5^k+n-1, 5)]) - 3*10^k}; \\ A014261
lista(nn) = my(list=List()); forstep (e=2, 8, 2, if (#select(x->(x%2), digits(e^2)) == 0, listput(list, e));); for (n=1, nn, my(o=odd(n)); forstep (e=0, 8, 2, my(oe = 10*o+e); if (#select(x->(x%2), digits(oe^2)) == 0, listput(list, oe)););); Vec(list); \\ Michel Marcus, Jun 25 2025

from itertools import count, product, islice
def A385300_gen(): # generator of terms
    for l in count(1):
        for d in product('13579',repeat=l):
            m = int(''.join(d))-1
            if m>0 and set(str(m**2))<={'0','2','4','6','8'}:
                yield m
A385300_list = list(islice(A385300_gen(),29)) # Chai Wah Wu, Jun 25 2025

A085586 n, n^2 and n^3 all use only even digits.

Original entry on oeis.org

0, 2, 20, 200, 202, 2000, 2002, 2020, 20000, 20002, 20020, 20200, 200000, 200002, 200020, 200200, 202000, 2000000, 2000002, 2000020, 2000200, 2002000, 2020000, 20000000, 20000002, 20000020, 20000200, 20000202, 20002000, 20002002, 20020000

Offset: 1

Zak Seidov, Jul 06 2003

Subsequence of A014263 and of A136904. - Michel Marcus, Oct 04 2013

			202 is a term because 202, 202^2=4008004 and 202^3=8024024008 all use only even digits.

Cf. A068690.

evdigs(n) = {if (n==0, return (1)); digs = digits(n); for (i = 1, #digs, if (digs[i] % 2, return (0));); return (1);}
isok(n) = evdigs(n) && evdigs(n^2) && evdigs(n^3); \\ Michel Marcus, Oct 04 2013

More terms from Michel Marcus and Jon E. Schoenfield, Oct 04 2013

cp's OEIS Frontend

A256708 Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 8 as largest digit.

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A030097 Numbers k such that k^2 has only even digits.

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A385300 Integers k containing only odd digits, except the last digit, such that k^2 is composed of only even digits.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

A085586 n, n^2 and n^3 all use only even digits.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

Extensions