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%I #41 Nov 19 2024 01:07:58
%S 7,11,13,17,23,29,31,37,41,43,53,59,67,71,73,79,83,97,101,107,109,127,
%T 137,149,151,163,167,181,193,197,199,211,227,233,239,241,251,263,277,
%U 281,283,307,317,337,349,353,359,367,379,389,401,409,419,431,433,449
%N Both p and p+30 are primes.
%C 30 = A002110(3) is the 3rd primorial number.
%C p and p+30 are not necessarily consecutive primes. Initial segment of A045320 is identical, but 113 is not in this sequence because 113 + 30 = 143 is divisible by 13.
%H Harvey P. Dale, <a href="/A049481/b049481.txt">Table of n, a(n) for n = 1..10000</a>
%H Hugo Pfoertner, <a href="/A049481/a049481.png">Observed ratio n*log(a(n))/pi(a(n))</a> for n=10^7..5.6*10^9 with a conjectured extrapolation for large n (2024).
%F Assuming Polignac's conjecture and the first Hardy-Littlewood conjecture: Limit_{n->oo} n*log(a(n))/primepi(a(n)) = (16/3)*A005597 = 3.52086... . - _Alain Rocchelli_, Oct 29 2024
%e Both 7 and 7 + 2*3*5 = 37 are prime.
%t lst={};Do[p=Prime[n];If[PrimeQ[p+30],AppendTo[lst,p]],{n,6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 04 2009 *)
%t Select[Prime[Range[100]],PrimeQ[#+30]&] (* _Harvey P. Dale_, Apr 28 2012 *)
%Y Cf. A045320, A001359, A005597, A023201.
%Y Cf. A049482, A049485, A049481, A154114. - _Vladimir Joseph Stephan Orlovsky_, Jan 04 2009
%K nonn
%O 1,1
%A _Labos Elemer_