A062066 a(1) = 2; a(n) is the smallest prime > a(n-1) such that a(n) + a(n-1) is a cube.

2, 727, 2017, 11807, 15193, 39679, 70913, 124199, 314777, 1090151, 1895833, 3017167, 4982833, 8841167, 10841833, 14570351, 17587081, 24557111, 26095889, 27061487, 32257513, 45051263, 46073737, 61776439, 72441289, 74756663, 82707337, 114430031, 157667761, 170841239

Offset

1,1

Links

Zak Seidov, Table of n, a(n) for n = 1..10000 (first 45 terms from Harry J. Smith)

Example

The next term after 727 is 2017 as 727 + 2017 = 2744 = 14^3.

Mathematica

a=2; s={a}; c=1; k=1; Do[Label[ne]; If[PrimeQ[b=k^3-a]&&b>a, a=b; c++; AppendTo[s, a]; If[c==10000, Break[]]]; k++; Goto[ne], {1}]; s (*Zak Seidov, Sep 28 2011*)
sp[n_]:=Module[{c=Floor[Surd[NextPrime[2n], 3]]+1}, While[!PrimeQ[ c^3- n], c++]; c^3-n]; NestList[sp, 2, 30] (* Harvey P. Dale, Dec 19 2015 *)

Prog

(PARI) iscube(x)= { f=factor(x)~; for(i=1, length(f), if (t=f[2, i]%3, return(0))); return(1); } { a=2; for (n=1, 45, a1=a; if (n>1, until (iscube(a + a1), a=nextprime(a + 1))); write("b062066.txt", n, " ", a) ) } \\ Harry J. Smith, Jul 31 2009

Crossrefs

Cf. A062064.

Sequence in context: A156008 A103169 A082438 * A174368 A082621 A053600

Adjacent sequences: A062063 A062064 A062065 * A062067 A062068 A062069

Keyword

nonn

Author

Amarnath Murthy, Jun 12 2001

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 21 2001

Further terms from Philip Sung (phil(AT)main.nu), Sep 11 2001

Status

approved