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

Author

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

Keywords

• nonn

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]

Examples

			(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
		

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

Crossrefs

Cf. A000040, A168147, A167535.

Programs

Mathematica

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

PARI

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