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Search: id:A137365
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| A137365 |
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Prime numbers n such that n = p1^3 + p2^3 + p3^3, a sum of cubes of 3 distinct prime numbers. |
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+0
4
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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Numbers n may have multiple decompositions; for example n=185527 and n=451837 have two, 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 (www.univ-ag.fr/~mhasler), 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.
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LINKS
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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.
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FORMULA
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A137365 = A000040 intersect A138853 = A000040 intersect A138854. - M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 13 2008
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EXAMPLE
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1483=3^3+5^3+11^3, 5381=17^3+7^3+5^3, 6271=3^3+11^3+17^3, etc.
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MAPLE
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(Maple code from R. J. Mathar) 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:
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MATHEMATICA
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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]]
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 (rgwv(AT)rgwv.com), Apr 13 2008
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PROGRAM
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(PARI) c=0; forprime(p=1, 10^6, isA138853(p) & write("b137365.txt", c++, " ", p)) - M. F. Hasler (www.univ-ag.fr/~mhasler), Apr 13 2008
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CROSSREFS
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Cf. A137366.
Cf. A024975 (a^3+b^3+c^3, a>b>c>0), A122723 (primes in A024975), A138853-A138854.
Adjacent sequences: A137362 A137363 A137364 this_sequence A137366 A137367 A137368
Sequence in context: A052167 A097024 A035864 this_sequence A137366 A045008 A104742
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KEYWORD
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nonn
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 09 2008
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EXTENSIONS
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Corrected and extended by Zak Seidov (zakseidov(AT)yahoo.com), R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 12 2008
Further edits by R. J. Mathar and njas, Jun 07 2008
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