A029776 -id:A029776 - cp's OEIS frontend

A029780 Numbers k such that every digit that appears in k also appears at least once in both k^2 and k^3.

0, 1, 5, 6, 10, 11, 25, 50, 55, 60, 64, 66, 76, 99, 100, 101, 110, 111, 112, 115, 116, 125, 225, 250, 275, 288, 323, 376, 405, 499, 500, 501, 502, 525, 550, 555, 600, 602, 625, 640, 642, 644, 660, 666, 676, 724, 726, 733, 755, 760, 776, 777, 833

Offset: 1

Patrick De Geest

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

Cf. A029772, A046827.

Select[Range[0,1000],Min[DigitCount[#^2,10,IntegerDigits[#]]]>0 && Min[ DigitCount[ #^3,10, IntegerDigits[#]]]>0&] (* Harvey P. Dale, Aug 12 2016 *)

from itertools import count, islice
def A029780_gen(startvalue=0): # generator of terms >= startvalue
    return filter(lambda n:set(str(n)) <= set(str(m:=n**2)) & set(str(n*m)), count(max(startvalue,0)))
A029780_list = list(islice(A029780_gen(),20)) # Chai Wah Wu, Apr 03 2023

A029772 intersect A029776. - Sean A. Irvine, Mar 04 2020

A030080 Primes p such that digits of p appear in p^3.

Original entry on oeis.org

5, 11, 29, 59, 61, 67, 71, 73, 97, 101, 109, 137, 151, 191, 229, 233, 251, 281, 311, 331, 337, 347, 389, 401, 449, 467, 499, 541, 619, 641, 683, 701, 719, 733, 751, 769, 787, 829, 881, 883, 887, 919, 947, 977, 991, 997, 1009, 1013, 1019, 1021

Offset: 1

Patrick De Geest

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

Primes in A029776.

Cf. A030082.

Select[Prime[Range[200]],Intersection[IntegerDigits[#],IntegerDigits[#^3]]==Union[IntegerDigits[#]]&] (* Harvey P. Dale, Apr 23 2025 *)

Offset changed by Andrew Howroyd, Aug 13 2024

A029777 Cubes k such that digits of cube root of k appear in k.

Original entry on oeis.org

0, 1, 64, 125, 216, 729, 1000, 1331, 1728, 9261, 13824, 15625, 24389, 32768, 35937, 39304, 59319, 64000, 85184, 117649, 125000, 132651, 157464, 166375, 175616, 205379, 216000, 226981, 262144, 274625, 287496, 300763, 357911

Offset: 1

Patrick De Geest

Harvey P. Dale, Table of n, a(n) for n = 1..10000

Cf. A029776.

Select[Range[0,100]^3,SubsetQ[IntegerDigits[#],IntegerDigits[CubeRoot[#]]]&] (* Harvey P. Dale, Jul 01 2025 *)

a(n) = A029776(n)^3. - Andrew Howroyd, Aug 11 2024

Offset corrected by Andrew Howroyd, Aug 11 2024

A064931 Numbers m such that the digits of m are also digits of m^3.

Original entry on oeis.org

1, 4, 5, 6, 9, 10, 11, 12, 21, 24, 25, 29, 32, 33, 34, 39, 40, 49, 50, 51, 54, 56, 59, 60, 61, 64, 65, 67, 71, 72, 73, 75, 76, 90, 97, 99, 100, 101, 102, 106, 109, 110, 114, 119, 120, 124, 125, 129, 137, 153, 176, 201, 202, 210, 212, 224, 228, 231, 233, 236

Offset: 1

Joseph L. Pe, Feb 14 2002

Presumably if a digit d appears k times in m, then it should appear at least k times in m^3. - N. J. A. Sloane, Nov 24 2018

			12^3 = 1728, which contains all digits of 12, so 12 is a term of the sequence.

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

Cf. A029776.

Select[Range[400],Min[DigitCount[#^3]-DigitCount[#]]>-1&] (* Harvey P. Dale, Nov 24 2018 *)

Corrected and Mathematica program replaced by Harvey P. Dale, Nov 24 2018

A074913 Digits of n appear in n^2 and in n^3.

Original entry on oeis.org

0, 1, 5, 6, 10, 11, 25, 50, 60, 64, 76, 100, 101, 110, 125, 250, 275, 376, 405, 500, 501, 502, 600, 602, 625, 640, 642, 724, 726, 760, 946, 963, 976, 996, 1000, 1001, 1005, 1006, 1010, 1021, 1025, 1050, 1060, 1100, 1171, 1201, 1205, 1250, 1258, 1421, 1465

Offset: 0

Zak Seidov, Oct 01 2002

From first 1000 n = 0 - 999, there are 34 such n, sharing their digits with n^2 and n^3. From first 100000 n = 0 - 999999, there are 1650 such n.

			n = 963, n^2 = 927369 -> 927(369), n^3 = 893056347 -> 8(9)305(63)47.

Cf. A046827, A029776.

cp's OEIS Frontend

A029780 Numbers k such that every digit that appears in k also appears at least once in both k^2 and k^3.

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A030080 Primes p such that digits of p appear in p^3.

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A029777 Cubes k such that digits of cube root of k appear in k.

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A064931 Numbers m such that the digits of m are also digits of m^3.

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A074913 Digits of n appear in n^2 and in n^3.

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