A168219 - OEIS

%I #16 Jan 26 2021 10:50:45

%S 1,3,4,6,15,16,18,24,27,30,31,36,37,43,51,52,57,60,73,75,81,82,87,90,

%T 93,106,108,109,114,145,154,159,160,163,165,171,174,175,178,196,201,

%U 204,207,208,211,220,222,225,228,234

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

%C It is conjectured that sequence is infinite.

%C 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]

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

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

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

%H G. C. Greubel, <a href="/A168219/b168219.txt">Table of n, a(n) for n = 1..1139</a>

%e (1) 1+10*1^3=11 gives a(1)=1

%e (2) 1+10*3^3=271=3^4 gives a(2)=3

%e (3) 1+10*37^3=506531 gives a(13)=37

%t Select[Range[100], PrimeQ[1 + 10*#^3] &] (* _G. C. Greubel_, Jul 16 2016 *)

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

%Y Cf. A000040, A168147, A167535.

%K nonn

%O 1,2

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