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.

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A138556 Numbers in A137365 but not in A137366.

Original entry on oeis.org

36161, 36583, 56897, 59093, 67733, 69073, 74177, 81901, 98533, 98837, 104021, 110629, 110879, 110933, 149759, 155861, 157933, 173087, 173293, 175463, 179999, 199081, 207719, 217573, 223919, 229321, 235171, 235243, 240479
Offset: 1

Views

Author

Robert G. Wilson v, Apr 13 2008

Keywords

A137365 Prime numbers n such that n = p1^3 + p2^3 + p3^3, a sum of cubes of 3 distinct prime numbers.

Original entry on oeis.org

1483, 5381, 6271, 7229, 9181, 11897, 13103, 13841, 14489, 17107, 20357, 25747, 26711, 27917, 30161, 30259, 31247, 32579, 36161, 36583, 36677, 36899, 36901, 42083, 48817, 54181, 55511, 55691, 56377, 56897, 57637, 59093, 64151, 66347
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Apr 09 2008

Keywords

Comments

Numbers n may have multiple decompositions; for example, n=185527 and n=451837 have two, and n=8627527 and n=32816503 have three. The smallest n with more than one decomposition is n = 185527 = 13^3+43^3+47^3 = 19^3+31^3+53^3, the 94th in the sequence. - R. J. Mathar, May 01 2008
Primes in A138853 and A138854. - M. F. Hasler, Apr 13 2008
The least prime, p, which has n decompositions {with its primes} is 1483 = {3, 5, 11}; 185527 = {13, 43, 47} & {19, 31, 53}; 8627527 = {19, 151, 173}, {33, 139, 181} & {71, 73, 199} and 1122871751 = {113, 751, 887}, {131, 701, 919}, {151, 659, 941} & {29, 107, 1039}. - Robert G. Wilson v, May 04 2008
The number of terms < 10^n: 0, 0, 0, 5, 56, 327, 2172, 13417, 86264, 567211, ..., . - Robert G. Wilson v, May 04 2008
The number of decompositions < 10^n: 0, 0, 0, 5, 56, 330, 2201, 13609, 87200, 571770, ..., . - Robert G. Wilson v, May 04 2008

Examples

			1483=3^3+5^3+11^3, 5381=17^3+7^3+5^3, 6271=3^3+11^3+17^3, etc.

Links

Crossrefs

Cf. A137366.
Cf. A024975 (a^3+b^3+c^3, a>b>c>0), A122723 (primes in A024975), A138853-A138854.

Programs

  • Maple
    # From R. J. Mathar: (Start)
isA030078 := proc(n) local cbr; cbr := floor(root[3](n)) ; if cbr^3 = n and isprime(cbr) then true ; else false; fi ; end:
isA137365 := proc(n) local p1,p2,p3,p3cub ; if isprime(n) then p1 := 2 ; while p1^3 <= n-16 do p2 := nextprime(p1) ; while p1^3+p2^3 <= n-8 do p3cub := n-p1^3-p2^3 ; if p3cub> p2^3 and isA030078(p3cub) then RETURN(true) ; fi ; p2 := nextprime(p2) ; od: p1 := nextprime(p1) ; od; RETURN(false) ; else RETURN(false) ; fi ; end:
for i from 1 do if isA137365( ithprime(i)) then printf("%d\n",ithprime(i)) ; fi ; od:
# (End)
  • Mathematica
    Array[r, 99]; Array[y, 99]; For[i = 0, i < 10^2, r[i] = y[i] = 0; i++ ]; z = 4^2; n = 0; For[i1 = 1, i1 < z, a = Prime[i1]; a2 = a^3; For[i2 = i1 + 1, i2 < z, b = Prime[i2]; b2 = b^3; For[i3 = i2 + 1, i3 < z, c = Prime[i3]; c2 = c^3; p = a2 + b2 + c2; If[PrimeQ[p], Print[a2, " + ", b2, " + ", c2, " = ", p]; n++; r[n] = p]; i3++ ]; i2++ ]; i1++ ]; Sort[Array[r, 88]] (* Vladimir Joseph Stephan Orlovsky *)
lst = {}; Do[p = Prime[q]^3 + Prime[r]^3 + Prime[s]^3; If[PrimeQ@ p, AppendTo[lst, p]], {q, 13}, {r, q - 1}, {s, r - 1}]; Take[Sort@ lst, 36] (* Robert G. Wilson v, Apr 13 2008 *)
nn=20; lim=Prime[nn]^3+3^3+5^3; Union[Select[Total[#^3]& /@ Subsets[Prime[Range[2,nn]], {3}], #Harvey P. Dale, Jan 15 2011 *)
  • PARI
    c=0; forprime(p=1,10^6, isA138853(p) & write("b137365.txt",c++," ",p)) \\ M. F. Hasler, Apr 13 2008

Formula

A137365 = A000040 intersect A138853 = A000040 intersect A138854. - M. F. Hasler, Apr 13 2008

Extensions

Corrected and extended by Zak Seidov, R. J. Mathar and Robert G. Wilson v, Apr 12 2008
Further edits by R. J. Mathar and N. J. A. Sloane, Jun 07 2008
Showing 1-2 of 2 results.

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