A172365 - OEIS

%I #17 Jan 22 2017 13:33:59

%S 3,5,7,7,11,19,11,17,31,47,71,139,67,101,199,71,107,211,127,191,379,

%T 167,251,499,211,317,631,307,461,919,347,521,1039,431,647,1291,467,

%U 701,1399,587,881,1759,727,1091,2179,907,1361,2719,911,1367,2731,991,1487,2971

%N List of primes p1, p2 and p3 such that 3*p1 - 2 = 2*p2 - 3 = p3.

%H Robert Israel, <a href="/A172365/b172365.txt">Table of n, a(n) for n = 1..9999</a>

%e a(1) = 3 = p1, a(2) = 5 = p2, a(3) = 7 = p3 because 3*3 - 2 = 2*5 - 3 = 7;

%e a(4) = 11 = p1, a(5) = 17 = p2, a(6) = 31 = p3 because 3*11 - 2 = 2*17 - 3 = 31.

%p for n from 1 to 500 do p1 := ithprime(n) ; p3 := 3*p1-2 ; if isprime(p3) then p2 := (p3+3)/2 ; if isprime(p2) then printf("%d,%d,%d,",p1,p2,p3) ; end if; end if; end do: # _R. J. Mathar_, May 02 2010

%t Flatten[Select[Tuples[Prime[Range[450]],{3}],3First[#]-2==2#[[2]]-3== Last[#]&]] (* _Harvey P. Dale_, Jun 02 2011 *)

%Y Cf. A000040, A172287, A172888.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Feb 01 2010

%E Corrected (triples 7,11,19 and 167,251,499 inserted) and extended by _R. J. Mathar_, May 02 2010