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 A137365 Prime numbers n such that n = p1^3 + p2^3 + p3^3, a sum of cubes of 3 distinct prime numbers. 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..13418 (duplicates omitted) Robert G. Wilson v, Table of n, a(n) for n = 1..13610 (duplicates included) Index to sequences related to sums of cubes. FORMULA A137365 = A000040 intersect A138853 = A000040 intersect A138854. - M. F. Hasler, Apr 13 2008 EXAMPLE 1483=3^3+5^3+11^3, 5381=17^3+7^3+5^3, 6271=3^3+11^3+17^3, etc. 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}], #b>c>0), A122723 (primes in A024975), A138853-A138854. Sequence in context: A238253 A035864 A255087 * A137366 A045008 A327880 Adjacent sequences: A137362 A137363 A137364 * A137366 A137367 A137368 KEYWORD nonn AUTHOR Vladimir Joseph Stephan Orlovsky, Apr 09 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 STATUS approved

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Last modified June 14 14:45 EDT 2024. Contains 373400 sequences. (Running on oeis4.)