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 1-4 of 4 results.

A126657 Prime numbers that are the sum of three distinct positive fourth powers.

Original entry on oeis.org

353, 1553, 5393, 6833, 7187, 7793, 7873, 8963, 9043, 9587, 10337, 11953, 13697, 14177, 14723, 16193, 17123, 20753, 21283, 21377, 21617, 23603, 25457, 28643, 29873, 30113, 30817, 31393, 35393, 35747, 39857, 43283, 45233, 45377, 46273
Offset: 1

Views

Author

Tomas Xordan, Feb 09 2007

Keywords

Examples

			1553= 1^4 + 4^4 + 6^4 = 1 + 256 + 1296.
6833 = 2^4 + 4^4 + 9^4 = 16 + 256 + 6561.
21377 = 2^4 + 5^4 + 12^4 = 16 + 625 + 20736.
35747 = 5^4 + 9^4 + 13^4 = 625 + 6561 + 28561.

Crossrefs

Cf. A125516, A126658.

Programs

  • Mathematica
    Union[Select[Total/@Subsets[Range[20]^4,{3}],PrimeQ]] (* Harvey P. Dale, May 08 2012 *)
  • PARI
    {m=15;p=m^4;v=vector(m,x,x^4);w=[];for(i=1,m-2,for(j=i+1,m-1, for(k=j+1,m,if((n=v[i]+v[j]+v[k])

Extensions

Edited, corrected and extended by Klaus Brockhaus, Feb 11 2007

A125516 Prime numbers that are the sum of three distinct positive squares.

Original entry on oeis.org

29, 41, 53, 59, 61, 83, 89, 101, 107, 109, 113, 131, 137, 139, 149, 157, 173, 179, 181, 197, 211, 227, 229, 233, 241, 251, 257, 269, 277, 281, 283, 293, 307, 313, 317, 331, 337, 347, 349, 353, 373, 379, 389, 397, 401, 409, 419, 421, 433, 443, 449, 457, 461
Offset: 1

Views

Author

Tomas Xordan, Jan 21 2007

Keywords

Examples

			29 = 2^2 + 3^2 + 4^2 = 4 + 9 + 16.
89 = 2^2 + 6^2 + 7^2 = 4 + 36 + 49; also 89 = 3^2 + 4^2 + 8^2 = 9 + 16 + 64.
353 = 2^2 + 5^2 + 18^2 = 4 + 25 + 324; also 353 = 4^2 + 9^2 + 16^2 = 16 + 81 + 256.

Links

Crossrefs

Cf. A088348, A126657, A126658.

Programs

  • Mathematica
    Select[Total/@Subsets[Range[20]^2,{3}],PrimeQ]//Union (* Harvey P. Dale, Aug 12 2025 *)
  • PARI
    {m=22;p=m^2;v=vector(m,x,x^2);w=[];for(i=1,m-2,for(j=i+1,m-1,for(k=j+1,m,if((n=v[i]+v[j]+v[k])

Extensions

Edited, corrected and extended by Klaus Brockhaus, Feb 11 2007

A126708 Prime numbers that are the sum of the cubes of three distinct primes with the same final digit.

Original entry on oeis.org

93871, 100043, 159389, 161071, 236627, 240551, 297233, 325693, 409499, 456623, 468551, 524287, 550061, 583981, 614683, 617401, 653491, 705277, 722807, 800171, 968239, 1016839, 1040311, 1129013, 1172261, 1276039, 1317259, 1326277, 1379519
Offset: 1

Views

Author

Tomas Xordan, Feb 11 2007

Keywords

Examples

			93871 = 13^3 + 23^3 + 43^3 = 2197 + 12167 + 79507 is prime and 13, 23, 43 are primes with the same final digit, hence 93871 is a term.
617401 = 43^3 + 53^3 + 73^3 = 79507 + 148877 + 389017 is prime and 43, 53, 73 are primes with the same final digit, hence 617401 is a term.
14391 = 3^3 + 13^3 + 23^3 = 27 + 2197 + 12167 is not prime; although 3, 13, 23 are primes with the same final digit, 14391 is not in the sequence.

Links

Crossrefs

Cf. A125516, A126657, A126658.

Programs

  • PARI
    {m=116; p=m^3; w=[]; forprime(i=1, m-2, r=i%10; forprime(j=i+1, m-1, forprime(k=j+1, m, if(j%10==r&&k%10==r&&(n=i^3+j^3+k^3)

Extensions

Edited, corrected and extended by Klaus Brockhaus, Feb 16 2007

A126704 Prime numbers that are the sum of three distinct positive sixth powers.

Original entry on oeis.org

4889, 50753, 51481, 66377, 262937, 308801, 797681, 840241, 1000793, 1046657, 1772291, 2303003, 2986777, 3032641, 3107729, 3365777, 4757609, 4804201, 5135609, 7530329, 7534361, 8061041, 8065073, 10516249, 12394721, 14638753
Offset: 1

Views

Author

Tomas Xordan, Feb 11 2007

Keywords

Examples

			4889 = 2^6 + 3^6 + 4^6 = 64 + 729 + 4096.
66377 = 4^6 + 5^6 + 6^6 = 4096 + 15625 + 46656.

Links

Crossrefs

Cf. A125516, A126657, A126658.

Programs

  • Maple
    N:= 10^10; # to find all terms <= N
A := {}:
for a from 1 to iroot(N,6) do
  for b from 1 to a-1 while a^6 + b^6 < N do
    for c from (a+b) mod 2 + 1 to b-1 by 2 do
      r:= a^6 + b^6 + c^6;
      if r > N then break fi;
      if isprime(r) then A:= A union {r} fi;
od od od:
sort(convert(A,list)); # Robert Israel, Dec 15 2015
  • Mathematica
    Union[Select[Total/@Subsets[Range[20]^6,{3}],PrimeQ]] (* Harvey P. Dale, Apr 20 2013 *)
  • PARI
    {m=16; p=m^6; w=[]; for(i=1,m-2,for(j=i+1, m-1, for(k=j+1, m, if((n=i^6+j^6+k^6)Klaus Brockhaus, Feb 16 2007 */

Extensions

Edited, corrected and extended by Klaus Brockhaus, Feb 16 2007
Showing 1-4 of 4 results.

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

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