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
KEYWORD
nonn
AUTHOR
Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 20 2009
STATUS
approved