

A168219


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


8



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
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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, SpringerVerlag NewYork 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: A137820 A049892 A063477 * A129827 A325179 A308533
Adjacent sequences: A168216 A168217 A168218 * A168220 A168221 A168222


KEYWORD

nonn


AUTHOR

EvaMaria Zschorn (em.zschorn(AT)zaschendorf.km3.de), Nov 20 2009


STATUS

approved



