A168219 Naturals n for which 1 + 10*n^3 (A168147) is prime.

1, 3, 4, 6, 15, 16, 18, 24, 27, 30, 31, 36, 37, 43, 51, 52, 57, 60, 73, 75, 81, 82, 87, 90, 93, 106, 108, 109, 114, 145, 154, 159, 160, 163, 165, 171, 174, 175, 178, 196, 201, 204, 207, 208, 211, 220, 222, 225, 228, 234

Offset

1,2

Comments

It is conjectured that sequence is infinite.

No three consecutive integers n are in the list. [Proof: An integer of the form n=3*k+2 generates 1+10*n^3 = 9*(9+30*k^3+60*k^2+40*k) which is divisible through 9, hence not a prime, so these n are not in the list. Since every third integer is of this form == 2 (mod 3), no more than two consecutive integers can be in the sequence.] [Zak Seidov, Nov 24 2009]

References

Harold Davenport, Multiplicative Number Theory, Springer-Verlag New-York 1980.

Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005.

Paulo Ribenboim, The New Book of Prime Number Records, Springer 1996.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1139

Example

(1) 1+10*1^3=11 gives a(1)=1
(2) 1+10*3^3=271=3^4 gives a(2)=3
(3) 1+10*37^3=506531 gives a(13)=37

Mathematica

Select[Range[100], PrimeQ[1 + 10*#^3] &] (* G. C. Greubel, Jul 16 2016 *)

Prog

(PARI) for(n=1, 2e2, isprime(n^3*10+1) && print1(n", "))  \\ M. F. Hasler, Jul 24 2011

Crossrefs

Cf. A000040, A168147, A167535.

Sequence in context: A049892 A346504 A063477 * A129827 A325179 A308533

Adjacent sequences: A168216 A168217 A168218 * A168220 A168221 A168222

Keyword

nonn

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 20 2009

Status

approved