A162218 -id:A162218 - cp's OEIS frontend

A046761 Largest number that is equal to sum of n-th powers of its digits.

1, 9, 1, 407, 9474, 194979, 548834, 14459929, 88593477, 912985153, 4679307774, 94204591914, 1, 564240140138, 28116440335967, 1, 4338281769391371, 35875699062250035, 1, 4929273885928088826, 63105425988599693916

Offset: 0

David W. Wilson

Joseph Myers, Table of n, a(n) for n = 0..107

Cf. A023052, A003321, A046074, A005188.

In other bases: A162218 (base 3), A162221 (base 4), A162224 (base 5), A162227 (base 6), A162230 (base 7), A162233 (base 8), A162236 (base 9).

Cross-references edited by Joseph Myers, Jun 28 2009

A033835 Smallest number > 1 equal to sum of n-th powers of its base-3 digits, or 0 if no such number exists (written in base 10).

Original entry on oeis.org

2, 5, 17, 0, 33, 66, 386, 258, 513, 1026, 0, 16388, 57345, 16389, 196610, 262149, 0, 786438, 3145733, 6291461, 0, 29360132, 0, 67108871, 234881030, 201326601, 1207959557, 2415919109, 3758096387, 5368709130, 10737418245, 30064771083

Offset: 1

David W. Wilson

Joseph Myers, Table of n, a(n) for n = 1..3158

Cf. A162216, A162217, A162218. In other bases: A033836 (base 4), A033837 (base 5), A033838 (base 6), A033839 (base 7), A033840 (base 8), A033841 (base 9), A003321 (base 10). - Joseph Myers, Jul 07 2009

A162216 Base-3 perfect digital invariants (written in base 10): numbers equal to the sum of the k-th powers of their base-3 digits, for some k.

Original entry on oeis.org

0, 1, 2, 5, 8, 17, 33, 34, 65, 66, 67, 131, 258, 259, 386, 512, 513, 514, 1026, 1027, 2049, 2050, 3075, 3076, 4100, 16388, 16389, 16390, 57345, 57346, 65538, 65539, 196610, 262149, 262150, 458754, 458755, 786438, 786439, 1048581, 1048582, 1310724

Offset: 1

Joseph Myers, Jun 28 2009

Whenever 3|a(n), then a(n+1) = a(n) + 1 (for the same k). The first 6 terms are exactly all the base-3 narcissistic numbers (where k = number of base-3 digits). For these numbers in other bases b = 4, ..., 16 see A010344 - A161953. - M. F. Hasler, Nov 18 2019

Joseph Myers, Table of n, a(n) for n = 1..6130 (complete to 2000 base-3 digits)

Cf. A162217 (corresponding exponents), A033835, A162218. In other bases: A162219 (base 4), A162222 (base 5), A162225 (base 6), A162228 (base 7), A162231 (base 8), A162234 (base 9), A023052 (base 10).

select( is_A162216(n,b=3)={nn||return(s==n))}, [0..10^5]) \\ M. F. Hasler, Nov 21 2019

A162217 Corresponding exponents for A162216.

Original entry on oeis.org

1, 1, 1, 2, 2, 3, 5, 5, 5, 6, 6, 6, 8, 8, 7, 7, 9, 9, 10, 10, 9, 9, 10, 10, 10, 12, 14, 14, 13, 13, 14, 14, 15, 16, 16, 16, 16, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 20, 22, 22, 24, 24, 26, 26, 25, 26, 26, 27, 28, 29, 29, 29, 29, 30, 30, 31, 31, 32, 32, 32, 32, 33, 33, 33, 33, 33

Offset: 1

Joseph Myers, Jun 28 2009

Joseph Myers, Table of n, a(n) for n=1..6130

Cf. A162216, A033835, A162218. In other bases: A162220 (base 4), A162223 (base 5), A162226 (base 6), A162229 (base 7), A162232 (base 8), A162235 (base 9), A046074 (base 10).

A162221 Greatest integer equal to the sum of the n-th powers of its base-4 digits (written in base 10).

Original entry on oeis.org

1, 3, 1, 62, 243, 33, 922, 2699, 13125, 40393, 1, 2049, 1075174, 6401871, 1, 57592238, 129336777, 516822801, 1163047905, 524289, 1, 62770507831, 1, 8388609, 1, 847624153770, 1, 53379719265825, 183016755558795, 411784948543867

Offset: 0

Joseph Myers, Jun 28 2009

Joseph Myers, Table of n, a(n) for n=0..1886

Cf. A162219, A162220, A033836. In other bases: A162218 (base 3), A162224 (base 5), A162227 (base 6), A162230 (base 7), A162233 (base 8), A162236 (base 9), A046761 (base 10).

A162224 Greatest integer equal to the sum of the n-th powers of its base-5 digits (written in base 10).

Original entry on oeis.org

1, 4, 18, 118, 419, 308, 9113, 257, 66562, 1874374, 1, 1, 1, 338749352, 2415951874, 3264337734, 21690135624, 69236561678, 276040954847, 1, 4408512107192, 17665416905448, 70525678835838, 422589088112942, 1972301894061609

Offset: 0

Joseph Myers, Jun 28 2009

Joseph Myers, Table of n, a(n) for n=0..807

Cf. A162222, A162223, A033837. In other bases: A162218 (base 3), A162221 (base 4), A162227 (base 6), A162230 (base 7), A162233 (base 8), A162236 (base 9), A046761 (base 10).

A162227 Greatest integer equal to the sum of the n-th powers of its base-6 digits (written in base 10).

Original entry on oeis.org

1, 5, 1, 251, 1, 6197, 36140, 269458, 391907, 10067135, 1, 1, 1, 6170640875, 1, 124246559501, 1, 5341093125745, 19418246235419, 58598336876363, 196242885967642, 3359860808719207, 1, 36185564197761935

Offset: 0

Joseph Myers, Jun 28 2009

Joseph Myers, Table of n, a(n) for n=0..386

Cf. A162225, A162226, A033838. In other bases: A162218 (base 3), A162221 (base 4), A162224 (base 5), A162230 (base 7), A162233 (base 8), A162236 (base 9), A046761 (base 10).

A162230 Greatest integer equal to the sum of the n-th powers of its base-7 digits (written in base 10).

Original entry on oeis.org

1, 6, 45, 250, 1, 9286, 35411, 794376, 72865, 34403018, 9885773, 1500022495, 1, 28700208851, 1, 2352056093102, 1, 102340463411217, 1, 3123368686057682, 1, 132116164569671440, 402070508232683666, 5528252581301500133

Offset: 0

Joseph Myers, Jun 28 2009

Joseph Myers, Table of n, a(n) for n=0..214

Cf. A162228, A162229, A033839. In other bases: A162218 (base 3), A162221 (base 4), A162224 (base 5), A162227 (base 6), A162233 (base 8), A162236 (base 9), A046761 (base 10).

A162233 Greatest integer equal to the sum of the n-th powers of its base-8 digits (written in base 10).

Original entry on oeis.org

1, 7, 52, 433, 273, 25639, 212419, 2087646, 13606405, 40695508, 637339524, 6710775966, 32298119799, 497577637886, 268451841, 1002493281673, 66627168235658, 17180000257, 5190196317533094, 57033725899507007

Offset: 0

Joseph Myers, Jun 28 2009

Joseph Myers, Table of n, a(n) for n=0..168

Cf. A162231, A162232, A033840. In other bases: A162218 (base 3), A162221 (base 4), A162224 (base 5), A162227 (base 6), A162230 (base 7), A162236 (base 9), A046761 (base 10).

A162236 Greatest integer equal to the sum of the n-th powers of its base-9 digits (written in base 10).

Original entry on oeis.org

1, 8, 50, 1052, 1824, 65539, 36804, 5300099, 6287267, 156608074, 3302332571, 177148, 155896317510, 1212041747339, 2113843488367, 5752216689703, 320659684133768, 6774649666149786, 37860400025315399, 157971147790033100

Offset: 0

Joseph Myers, Jun 28 2009

Joseph Myers, Table of n, a(n) for n=0..124

Cf. A162234, A162235, A033841. In other bases: A162218 (base 3), A162221 (base 4), A162224 (base 5), A162227 (base 6), A162230 (base 7), A162233 (base 8), A046761 (base 10).

cp's OEIS Frontend

A046761 Largest number that is equal to sum of n-th powers of its digits.

Views

Author

Keywords

Links

Crossrefs

Extensions

A033835 Smallest number > 1 equal to sum of n-th powers of its base-3 digits, or 0 if no such number exists (written in base 10).

Views

Author

Keywords

Links

Crossrefs

A162216 Base-3 perfect digital invariants (written in base 10): numbers equal to the sum of the k-th powers of their base-3 digits, for some k.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A162217 Corresponding exponents for A162216.

Views

Author

Keywords

Links

Crossrefs

A162221 Greatest integer equal to the sum of the n-th powers of its base-4 digits (written in base 10).

Views

Author

Keywords

Links

Crossrefs

A162224 Greatest integer equal to the sum of the n-th powers of its base-5 digits (written in base 10).

Views

Author

Keywords

Links

Crossrefs

A162227 Greatest integer equal to the sum of the n-th powers of its base-6 digits (written in base 10).

Views

Author

Keywords

Links

Crossrefs

A162230 Greatest integer equal to the sum of the n-th powers of its base-7 digits (written in base 10).

Views

Author

Keywords

Links

Crossrefs

A162233 Greatest integer equal to the sum of the n-th powers of its base-8 digits (written in base 10).

Views

Author

Keywords

Links

Crossrefs

A162236 Greatest integer equal to the sum of the n-th powers of its base-9 digits (written in base 10).

Views

Author

Keywords

Links

Crossrefs