The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 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, 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 26 08:35 EDT 2022. Contains 356993 sequences. (Running on oeis4.)