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 1-3 of 3 results.

A123075 Smallest number expressible as the sum of three 4th powers in exactly n ways.

Original entry on oeis.org

1, 2673, 811538, 5978882, 137149922, 292965218, 779888018, 5745705602, 105760443698, 49511121842, 1872511131218, 281539574498, 17673688436978, 17873514984962, 253930825318898, 7865870969138, 768054952462322
Offset: 1

Views

Author

Tom Womack (tom(AT)womack.net), Sep 19 2006

Keywords

Crossrefs

Cf. A085559, A011541, A122540.

A193244 Numbers that are the sum of three biquadrates (fourth powers) in more than one way.

Original entry on oeis.org

16562, 28593, 35378, 43218, 54977, 94178, 106353, 122018, 134162, 137633, 149058, 181202, 195122, 198497, 235298, 235553, 264113, 264992, 300833, 318402, 324818, 364658, 384833, 439922, 457488, 462722, 514098, 522242, 566048, 611618, 624962
Offset: 1

Views

Author

M. F. Hasler, Jan 01 2013

Keywords

Comments

Erroneous version of A309762. - Ilya Gutkovskiy, Aug 15 2019
A subsequence of A003337. Lists the indices such that A193243(n) > 1.

Examples

			a(1) = 16562 = 1^4 + 9^4 + 10^4 = 5^4 + 6^4 + 11^4, and this is the least number having two such decompositions.

Crossrefs

Cf. A003337, A193243, A047714, A085559, A122540, A123075.

Programs

  • PARI
    is_A000404(n)={ for( i=1, #n=factor(n)~%4, n[1, i]==3 & n[2, i]%2 & return); n & ( vecmin(n[1, ])==1 || (n[1, 1]==2 & n[2, 1]%2))} \\ M. F. Hasler, Feb 07 2009
  • PARI
    for(n=1,9e9, is_A000404(n) && A193243(n)>1 && print1(n","))

A140834 Primes that are the sum of at most four nonzero 4th powers.

Original entry on oeis.org

2, 3, 17, 19, 83, 97, 113, 163, 179, 257, 337, 353, 419, 499, 593, 641, 643, 673, 769, 787, 881, 883, 1153, 1297, 1409, 1459, 1553, 1889, 2003, 2083, 2131, 2417, 2579, 2593, 2609, 2657, 2659, 2689, 2819, 3169, 3217, 3697, 3779, 3889, 3907, 4099, 4129, 4177
Offset: 1

Views

Author

Jonathan Vos Post, Jul 18 2008

Keywords

Comments

This sequence was checked by T. D. Noe, who had supplied the b-list for A004833. A037896 is a subset of {Primes that are the sum of at exactly 2 nonzero 4th powers}, itself a subset of A002645 Quartan primes: primes of the form x^4 + y^4, x>0, y>0.

Crossrefs

Cf. A000040, A000583, A002645, A003294, A004833, A037896, A085318, A122540, A126657, A133740.

Formula

A000040 INTERSECTION A004833. {A133740 = Primes that are the sum of at exactly 4 nonzero 4th powers} UNION {A085318 = Primes that are the sum of at exactly 3 nonzero 4th powers} UNION {A002645 = Primes that are the sum of at exactly 2 nonzero 4th powers}.

Extensions

Missing term 353 inserted by Georg Fischer, May 11 2024
Showing 1-3 of 3 results.

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

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