A003321 -id:A003321 - cp's OEIS frontend

A014576 Smallest n-digit narcissistic (or Armstrong) number: smallest n-digit number equal to sum of n-th powers of its digits (or 0 if no such number exists).

1, 0, 153, 1634, 54748, 548834, 1741725, 24678050, 146511208, 4679307774, 32164049650, 0, 0, 28116440335967, 0, 4338281769391370, 21897142587612075, 0, 1517841543307505039, 63105425988599693916, 128468643043731391252, 0

Offset: 1

N. J. A. Sloane

M. Gardner, The Magic Numbers of Dr Matrix. Prometheus, Buffalo, NY, 1985, p. 249.
C. A. Pickover, Keys to Infinity. New York: W. H. Freeman, pp. 169-170, 1995.

T. D. Noe, Table of n, a(n) for n=1..39 (complete sequence)
Harvey Heinz, Narcissistic Numbers
Mike Keith, Wild Narcissistic Numbers (Copy as of May 2008 on web.archive.org - page does not exist any more.)
Eric Weisstein's World of Mathematics, Narcissistic Number.

Cf. A001694, A007532, A005934, A005188, A003321, A023052, A046074.

(* This program is not suitable for more than 10 terms *) a[n_] := For[k = 10^(n-1), True, k++, If[k > 10^n - 1, Return[0], If[k == Total[ IntegerDigits[k]^IntegerLength[k] ], Return[k] ] ] ]; Table[ Print[an = a[n]]; an, {n, 1, 10}] (* Jean-François Alcover, Oct 15 2013 *)

Terms and links added by Patrick De Geest, Oct 1998

Broken links fixed by M. F. Hasler, Feb 12 2013

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

A033836 Smallest number > 1 equal to sum of n-th powers of its base-4 digits, or 0 if no such number exists (written in base 10).

Original entry on oeis.org

2, 0, 8, 83, 32, 922, 128, 7330, 512, 0, 2048, 1075174, 8192, 0, 32768, 86486662, 131072, 776413846, 524288, 0, 2097152, 0, 8388608, 0, 33554432, 0, 134217728, 183016755558795, 536870912, 1029465324149666, 2147483648

Offset: 1

David W. Wilson

Joseph Myers, Table of n, a(n) for n = 1..1887

Cf. A162219, A162220, A162221. In other bases: A033835 (base 3), A033837 (base 5), A033838 (base 6), A033839 (base 7), A033840 (base 8), A033841 (base 9), A003321 (base 10). - Joseph Myers, Jul 07 2009

A033837 Smallest number > 1 equal to sum of n-th powers of its base-5 digits, or 0 if no such number exists (written in base 10).

Original entry on oeis.org

2, 13, 28, 289, 308, 4890, 257, 66562, 322217, 0, 0, 0, 16387, 268533762, 2204944815, 172449032, 34876823313, 207708636457, 0, 3315971951065, 8837942823632, 53027623387338, 422589088112942, 1129785254793

Offset: 1

David W. Wilson

Joseph Myers, Table of n, a(n) for n = 1..809

Cf. A162222, A162223, A162224. In other bases: A033835 (base 3), A033836 (base 4), A033838 (base 6), A033839 (base 7), A033840 (base 8), A033841 (base 9), A003321 (base 10). - Joseph Myers, Jul 07 2009

A033838 Smallest number > 1 equal to sum of n-th powers of its base-6 digits, or 0 if no such number exists (written in base 10).

Original entry on oeis.org

2, 0, 99, 0, 308, 36140, 269458, 391907, 10067135, 0, 0, 0, 1428423394, 0, 32693825124, 0, 797557733967, 11512812322194, 58598336876363, 192937380661240, 1443716084981654, 0, 36185564197761935

Offset: 1

David W. Wilson

Joseph Myers, Table of n, a(n) for n=1..387

Cf. A162225, A162226, A162227. In other bases: A033835 (base 3), A033836 (base 4), A033837 (base 5), A033839 (base 7), A033840 (base 8), A033841 (base 9), A003321 (base 10). - Joseph Myers, Jul 07 2009

A033839 Smallest number > 1 equal to sum of n-th powers of its base-7 digits, or 0 if no such number exists (written in base 10).

Original entry on oeis.org

2, 10, 9, 0, 65, 35411, 37271, 72865, 2236488, 1110699, 416002778, 0, 5021821389, 0, 533453816220, 0, 18487285640920, 0, 1314916195476894, 0, 66773332795109537, 138809539743164589, 1591663132485308115, 14216271609499243850

Offset: 1

David W. Wilson

Joseph Myers, Table of n, a(n) for n=1..215

Cf. A162228, A162229, A162230. In other bases: A033835 (base 3), A033836 (base 4), A033837 (base 5), A033838 (base 6), A033840 (base 8), A033841 (base 9), A003321 (base 10). - Joseph Myers, Jul 07 2009

Extended by Joseph Myers, Jul 07 2009

A033840 Smallest number > 1 equal to sum of n-th powers of its base-8 digits, or 0 if no such number exists (written in base 10).

Original entry on oeis.org

2, 20, 92, 16, 1056, 212419, 128, 13379, 40695508, 1024, 4196352, 13892162580, 8192, 268451840, 1002493281672, 65536, 17180000256, 4998382669357032, 524288, 1099512676352, 3418993385062038719, 4194304, 70368752566272

Offset: 1

David W. Wilson

Joseph Myers, Table of n, a(n) for n=1..170

Cf. A162231, A162232, A162233. In other bases: A033835 (base 3), A033836 (base 4), A033837 (base 5), A033838 (base 6), A033839 (base 7), A033841 (base 9), A003321 (base 10). - Joseph Myers, Jul 07 2009

Extended by Joseph Myers, Jul 07 2009

A033841 Smallest number > 1 equal to sum of n-th powers of its base-9 digits, or 0 if no such number exists (written in base 10).

Original entry on oeis.org

2, 41, 27, 353, 243, 36804, 2187, 6287267, 19683, 403584750, 177147, 42256814922, 1594323, 1447031689954, 14348907, 320659684133768, 129140163, 117025292105903, 1162261467, 170554117891588216, 10460353203

Offset: 1

David W. Wilson

Joseph Myers, Table of n, a(n) for n=1..125

Cf. A162234, A162235, A162236. In other bases: A033835 (base 3), A033836 (base 4), A033837 (base 5), A033838 (base 6), A033839 (base 7), A033840 (base 8), A003321 (base 10). - Joseph Myers, Jul 07 2009

Extended by Joseph Myers, Jul 07 2009

A052464 Fixed points for operation of repeatedly replacing a number with the sum of the fifth power of its digits.

Original entry on oeis.org

0, 1, 4150, 4151, 54748, 92727, 93084, 194979

Offset: 1

Henry Bottomley, Mar 15 2000

Equivalently, numbers equal to the sum of 5th powers of their decimal digits. Since this sum is <= 9^5*d for a d-digit number n >= 10^(d-1), there cannot be such a number with more than 6 digits. - M. F. Hasler, Apr 12 2015

			a(2) = 4150 since 4^5 + 1^5 + 5^5 + 0^5 = 1024 + 1 + 3125 + 0 = 4150.

G. K. Patil, Ramanujan's Life And His Contributions In The Field Of Mathematics, International Journal of Scientific Research and Engineering Studies (IJSRES), 1(6) (2014), ISSN: 2349-8862.

Cf. A023052, A046074, A046197, A052455, A124068, A124069, A226970, A003321.

for(n=0,10^6,A055014(n)==n&&print1(n",")) \\ M. F. Hasler, Apr 12 2015

A124068 Fixed points for operation of repeatedly replacing a number with the sum of the seventh power of its digits.

Original entry on oeis.org

0, 1, 1741725, 4210818, 9800817, 9926315, 14459929

Offset: 1

Sébastien Dumortier, Nov 05 2006

The sequence "Fixed points for operation of repeatedly replacing a number by the sum of the sixth power of its digits" has just 3 terms: 0, 1, and 548834.

For a d-digit number n >= 10^(d-1), the sum of 7th powers of its digits is <= 9^7*d, therefore these numbers cannot exceed 41205040. - M. F. Hasler, Apr 12 2015

			1741725 = 1^7 + 7^7 + 4^7 + 1^7 + 7^7 + 2^7 + 5^7.

Cf. A046197, A052455, A052464, A124069, A226970, A003321.

isok(n) = my(d = digits(n)); sum(k=1, #d, d[k]^7) == n; \\ Michel Marcus, Feb 21 2015

for(n=0,41205040,A123253(n)==n&&print1(n",")) \\ M. F. Hasler, Apr 12 2015

cp's OEIS Frontend

A014576 Smallest n-digit narcissistic (or Armstrong) number: smallest n-digit number equal to sum of n-th powers of its digits (or 0 if no such number exists).

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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).

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A033836 Smallest number > 1 equal to sum of n-th powers of its base-4 digits, or 0 if no such number exists (written in base 10).

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A033837 Smallest number > 1 equal to sum of n-th powers of its base-5 digits, or 0 if no such number exists (written in base 10).

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A033838 Smallest number > 1 equal to sum of n-th powers of its base-6 digits, or 0 if no such number exists (written in base 10).

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A033839 Smallest number > 1 equal to sum of n-th powers of its base-7 digits, or 0 if no such number exists (written in base 10).

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A033840 Smallest number > 1 equal to sum of n-th powers of its base-8 digits, or 0 if no such number exists (written in base 10).

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A033841 Smallest number > 1 equal to sum of n-th powers of its base-9 digits, or 0 if no such number exists (written in base 10).

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A052464 Fixed points for operation of repeatedly replacing a number with the sum of the fifth power of its digits.

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PARI

A124068 Fixed points for operation of repeatedly replacing a number with the sum of the seventh power of its digits.

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PARI

PARI