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.
%I A137365 #32 Jan 31 2025 03:49:37
%S A137365 1483,5381,6271,7229,9181,11897,13103,13841,14489,17107,20357,25747,
%T A137365 26711,27917,30161,30259,31247,32579,36161,36583,36677,36899,36901,
%U A137365 42083,48817,54181,55511,55691,56377,56897,57637,59093,64151,66347
%N A137365 Prime numbers n such that n = p1^3 + p2^3 + p3^3, a sum of cubes of 3 distinct prime numbers.
%C A137365 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
%C A137365 Primes in A138853 and A138854. - _M. F. Hasler_, Apr 13 2008
%C A137365 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
%C A137365 The number of terms < 10^n: 0, 0, 0, 5, 56, 327, 2172, 13417, 86264, 567211, ..., . - _Robert G. Wilson v_, May 04 2008
%C A137365 The number of decompositions < 10^n: 0, 0, 0, 5, 56, 330, 2201, 13609, 87200, 571770, ..., . - _Robert G. Wilson v_, May 04 2008
%H A137365 Robert G. Wilson v, <a href="/A137365/b137365.txt">Table of n, a(n) for n = 1..13418</a> (duplicates omitted)
%H A137365 Robert G. Wilson v, <a href="/A137365/a137365.txt">Table of n, a(n) for n = 1..13610</a> (duplicates included)
%H A137365 <a href="/index/Su#ssq">Index to sequences related to sums of cubes</a>.
%F A137365 A137365 = A000040 intersect A138853 = A000040 intersect A138854. - _M. F. Hasler_, Apr 13 2008
%e A137365 1483=3^3+5^3+11^3, 5381=17^3+7^3+5^3, 6271=3^3+11^3+17^3, etc.
%p A137365 # From _R. J. Mathar_: (Start)
%p A137365 isA030078 := proc(n) local cbr; cbr := floor(root[3](n)) ; if cbr^3 = n and isprime(cbr) then true ; else false; fi ; end:
%p A137365 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:
%p A137365 for i from 1 do if isA137365( ithprime(i)) then printf("%d\n",ithprime(i)) ; fi ; od:
%p A137365 # (End)
%t A137365 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_ *)
%t A137365 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 *)
%t A137365 nn=20; lim=Prime[nn]^3+3^3+5^3; Union[Select[Total[#^3]& /@ Subsets[Prime[Range[2,nn]], {3}], #<lim && PrimeQ[#]&]] (* _Harvey P. Dale_, Jan 15 2011 *)
%o A137365 (PARI) c=0; forprime(p=1,10^6, isA138853(p) & write("b137365.txt",c++," ",p)) \\ _M. F. Hasler_, Apr 13 2008
%Y A137365 Cf. A137366.
%Y A137365 Cf. A024975 (a^3+b^3+c^3, a>b>c>0), A122723 (primes in A024975), A138853-A138854.
%K A137365 nonn
%O A137365 1,1
%A A137365 _Vladimir Joseph Stephan Orlovsky_, Apr 09 2008
%E A137365 Corrected and extended by _Zak Seidov_, _R. J. Mathar_ and _Robert G. Wilson v_, Apr 12 2008
%E A137365 Further edits by _R. J. Mathar_ and _N. J. A. Sloane_, Jun 07 2008