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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}], #<lim && PrimeQ[#]&]] (* Harvey P. Dale, Jan 15 2011 *)

PROG

(PARI) c=0; forprime(p=1, 10^6, isA138853(p) & write("b137365.txt", c++, " ", p)) \\ M. F. Hasler, Apr 13 2008

CROSSREFS

Cf. A137366.

Cf. A024975 (a^3+b^3+c^3, a>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 August 12 16:32 EDT 2022. Contains 356077 sequences. (Running on oeis4.)