cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 10 results.

A003321 Smallest n-th order perfect digital invariant or PDI: smallest number > 1 equal to sum of n-th powers of its digits, or 0 if no such number exists.

Original entry on oeis.org

2, 0, 153, 1634, 4150, 548834, 1741725, 24678050, 146511208, 4679307774, 32164049650, 0, 564240140138, 28116440335967, 0, 4338281769391370, 233411150132317, 0, 1517841543307505039, 63105425988599693916
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Except for the initial term, this is the third column of A252648. - M. F. Hasler, Feb 16 2015
a(n) = 0 if n>1 and in A262094. - Dmitry Kamenetsky, Jun 05 2020

Examples

			1^3 + 5^3 + 3^3 = 153.
1*0^17 + 5*1^17 + 2*2^17 + 4*3^17 + 1*4^17 + 1*5^17 + 1*7^17 = 233411150132317.

References

  • M. Gardner, The Magic Numbers of Dr Matrix. Prometheus, Buffalo, NY, 1985, p. 249.
  • J. S. Madachy, Mathematics on Vacation, Thomas Nelson and Sons Ltd. 1966, p. 164.
  • J. S. Madachy, Madachy's Mathematical Recreations, Dover, p. 164.
  • C. A. Pickover, Keys to Infinity. New York: W. H. Freeman, pp. 169-170, 1995.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A001694, A007532, A005934, A005188, A014576, A023052, A046074, A046761.
In other bases: A033835 (base 3), A033836 (base 4), A033837 (base 5), A033838 (base 6), A033839 (base 7), A033840 (base 8), A033841 (base 9).

Programs

  • PARI
    a(n)=m=1;while(m*9^n>=10^m,m++);for(k=2,10^m,d=digits(k);s=sum(i=1,#d,d[i]^n);if(s==k,return(k)));0
n=1;while(n<10,print1(a(n),", ");n++) \\ Derek Orr, Dec 19 2014

Extensions

Additional comments from Lekraj Beedassy, May 23 2001
Extended and 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

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

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

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

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

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

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

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

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

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

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

Extensions

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

Views

Author

David W. Wilson

Keywords

Links

Crossrefs

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

Extensions

Extended by Joseph Myers, Jul 07 2009

A162231 Base 8 perfect digital invariants (written in base 10): numbers equal to the sum of the k-th powers of their base-8 digits, for some k.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 16, 17, 20, 52, 92, 128, 129, 133, 256, 257, 272, 273, 307, 432, 433, 1024, 1025, 1056, 1057, 2323, 8192, 8193, 13379, 16384, 16385, 16512, 16513, 16819, 17864, 17865, 24583, 25639, 65536, 65537, 65792, 65793, 212419, 524288, 524289
Offset: 1

Views

Author

Joseph Myers, Jun 28 2009

Keywords

Comments

Whenever a(n) is a multiple of 8, then a(n+1) = a(n) + 1 is also a base 8 perfect digital invariant, with the same exponent k. - M. F. Hasler, Nov 21 2019

Links

Crossrefs

Cf. A162232 (corresponding exponents), A010354 (restriction to power = number of digits), A033840, A162233. In other bases: A162216 (base 3), A162219 (base 4), A162222 (base 5), A162225 (base 6), A162228 (base 7), A162234 (base 9), A023052 (base 10).

Programs

A162232 Corresponding exponents for A162231.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 2, 2, 3, 7, 7, 3, 4, 4, 4, 4, 3, 3, 3, 10, 10, 5, 5, 5, 13, 13, 8, 7, 7, 7, 7, 5, 5, 5, 5, 5, 16, 16, 8, 8, 6, 19, 19, 7, 7, 7, 10, 10, 10, 10, 7, 7, 8, 22, 22, 11, 11, 8, 25, 25, 9, 13, 13, 13, 13, 28, 28, 14, 14, 10, 10, 31, 31, 16, 16, 16, 16, 11, 12, 34, 34, 17
Offset: 1

Views

Author

Joseph Myers, Jun 28 2009

Keywords

Links

Crossrefs

Cf. A162231, A033840, A162233. In other bases: A162217 (base 3), A162220 (base 4), A162223 (base 5), A162226 (base 6), A162229 (base 7), A162235 (base 9), A046074 (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

Views

Author

Joseph Myers, Jun 28 2009

Keywords

Links

Crossrefs

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).
Showing 1-10 of 10 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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