A137110 -id:A137110 - cp's OEIS frontend

A137116 Numbers k such that k and k^2 use only the digits 2, 5, 7, 8 and 9.

5, 27, 77, 85, 527, 727, 7227, 9777, 28277, 29585, 88277, 99277, 278527, 298827, 2788527, 2789227, 5289227, 8875727, 9889277, 22925527, 27797977, 29879585, 52898827, 85298827, 88875527, 99789227, 99988777, 278889277, 287279585, 292898827, 297875527, 299929585, 527252527, 528982977, 727528527, 727825527, 727925527, 988579585, 992587527

Offset: 1

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

Generated with DrScheme.

			727872928279585^2 = 529798999722297889227927772225.

Michael S. Branicky, Table of n, a(n) for n = 1..578 (through 20 digits; first 180 terms from Jonathan Wellons)
Jonathan Wellons, Tables of Shared Digits [archived].

Cf. A137110, A137117.

# uses auptod in A137110
print(auptod(16, only="25789")) # Michael S. Branicky, May 27 2021

A137066 Numbers k such that k and k^2 use only the digits 2, 3, 4 and 5.

Original entry on oeis.org

2, 5, 235, 2335, 23335, 233335, 2333335, 2354235, 23333335, 233333335, 2333333335, 2333524235, 23333333335, 23333524235, 233333333335, 2333333333335, 23333333333335, 233333333333335, 2333333333333335, 23333333333333335, 233333333333333335

Offset: 1

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

Generated with DrScheme.
Contains 2*10^m + (10^m-1)/3 + 2 for m >= 2. Are these all the terms > 23333524235? There are no others with up to 25 digits. - Robert Israel, Jul 02 2018
There are no others than those of that form with up to 35 digits. - Michael S. Branicky, May 25 2021

			23333524235^2 = 544453353225332335225.

Jonathan Wellons, Tables of Shared Digits [archived].

Cf. A137110.

isokd(x) = (x < 2) || (x > 5);
isok(n) = !#select(x->isokd(x), digits(n)) && !#select(x->isokd(x), digits(n^2)); \\ Michel Marcus, Jul 02 2018

# uses auptod in A137110
print(auptod(16, only="2345")) # Michael S. Branicky, May 25 2021

A137093 Numbers k such that k and k^2 use only the digits 2, 4, 5 and 6.

Original entry on oeis.org

2, 5, 25, 65, 665, 6665, 66665, 666665, 6666665, 25625465, 65226242, 66666665, 666666665, 6666666665, 66666666665, 666666666665, 6666666666665, 66666666666665, 666666666666665, 6666666666666665, 66666666666666665, 666666666666666665, 6666666666666666665

Offset: 1

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

Generated with DrScheme.

Contains 6*(10^n - 1)/9 - 1 for n >= 1. There are no others than those of this form with up to 35 digits. - Michael S. Branicky, May 25 2021

			25625465^2 = 656664456466225.

Jonathan Wellons, Tables of Shared Digits [archived].

Cf. A137110.

fQ[n_] := Block[{d = DigitCount@ n}, Total@ Delete[d, {{2}, {4}, {5}, {6}}] == 0]; Select[Range@ 100000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, Apr 29 2015 *)

from itertools import product
A137093_list = [int(''.join(a)) for l in range(1,10) for a in product('2456',repeat = l) if set(str(int(''.join(a))**2)) <= {'2','4','5','6'}] # Chai Wah Wu, Apr 29 2015

# uses auptod in A137110
print(auptod(16, only="2456")) # Michael S. Branicky, May 25 2021

a(20)-a(23) from Michael S. Branicky, May 25 2021

A137117 Numbers k such that k and k^2 use only the digits 2, 5, 7 and 9.

Original entry on oeis.org

5, 27, 77, 527, 7227, 27797977

Offset: 1

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

Generated with DrScheme.
No further terms up to 10^12. - Harvey P. Dale, Oct 02 2017
No further terms up to 10^38. - Michael S. Branicky, May 27 2021

			27797977^2 = 772727525292529.

Jonathan Wellons, Tables of Shared Digits [archived].

Cf. A137110, A137116.

With[{c={2,5,7,9}},Table[Select[FromDigits/@Tuples[c,n],SubsetQ[c, IntegerDigits[ #^2]]&],{n,8}]]//Flatten (* Harvey P. Dale, Oct 02 2017 *)

# uses auptod in A137110
print(auptod(16, only="2579")) # Michael S. Branicky, May 27 2021

cp's OEIS Frontend

A137116 Numbers k such that k and k^2 use only the digits 2, 5, 7, 8 and 9.

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A137066 Numbers k such that k and k^2 use only the digits 2, 3, 4 and 5.

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A137093 Numbers k such that k and k^2 use only the digits 2, 4, 5 and 6.

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A137117 Numbers k such that k and k^2 use only the digits 2, 5, 7 and 9.

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Mathematica

Python