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A060229 Smaller member of a twin prime pair whose mean is a multiple of A002110(3)=30.

%I A060229 #36 Sep 08 2022 08:45:03
%S A060229 29,59,149,179,239,269,419,569,599,659,809,1019,1049,1229,1289,1319,
%T A060229 1619,1949,2129,2309,2339,2549,2729,2789,2969,2999,3119,3299,3329,
%U A060229 3359,3389,3539,3929,4019,4049,4229,4259,4649,4799,5009,5099,5279,5519,5639
%N A060229 Smaller member of a twin prime pair whose mean is a multiple of A002110(3)=30.
%C A060229 Equivalently, smaller of twin prime pair with primes in different decades.
%C A060229 Primes p such that p and p+2 are prime factors of Fibonacci(p-1) and Fibonacci(p+1) respectively. - _Michel Lagneau_, Jul 13 2016
%C A060229 The union of this sequence and A282326 gives A132243. - _Martin Renner_, Feb 11 2017
%C A060229 The union of {3,5}, A282321, A282323 and this sequence gives A001359. - _Martin Renner_, Feb 11 2017
%C A060229 The union of {3,5,7}, A282321, A282322, A282323, A282324, this sequence and A282326 gives A001097. - _Martin Renner_, Feb 11 2017
%C A060229 Number of terms less than 10^k, k=2,3,4,...: 2, 11, 72, 407, 2697, 19507, 146516, ... - _Muniru A Asiru_, Jan 29 2018
%H A060229 Muniru A Asiru, <a href="/A060229/b060229.txt">Table of n, a(n) for n = 1..1000</a>
%e A060229 For the pair {149,151} (149 + 151)/2 = 5*30.
%p A060229 isA060229 := proc(n)
%p A060229     if modp(n+1,30) =0 and isprime(n) and isprime(n+2) then
%p A060229         true;
%p A060229     else
%p A060229         false;
%p A060229     end if;
%p A060229 end proc:
%p A060229 A060229 := proc(n)
%p A060229     option remember;
%p A060229     if n =1 then
%p A060229         29;
%p A060229     else
%p A060229         for a from procname(n-1)+2 by 2 do
%p A060229             if isA060229(a) then
%p A060229                 return a;
%p A060229             end if;
%p A060229         end do:
%p A060229     end if;
%p A060229 end proc:
%p A060229 seq(A060229(n),n=1..80) ; # _R. J. Mathar_, Feb 19 2017
%t A060229 Select[Prime@ Range[10^3], PrimeQ[# + 2] && Mod[# + 1, 30] == 0 &] (* _Michael De Vlieger_, Jul 14 2016 *)
%o A060229 (PARI) isok(n) = isprime(n) && isprime(n+2) && !((n+1) % 30); \\ _Michel Marcus_, Dec 11 2013
%o A060229 (Magma) [p: p in PrimesUpTo(7000) | IsPrime(p+2) and p mod 30 eq 29 ]; // _Vincenzo Librandi_, Feb 13 2017
%o A060229 (GAP) Filtered(List([0..200], k -> 30*k-1), n -> IsPrime(n) and IsPrime(n+2));  # _Muniru A Asiru_, Feb 02 2018
%Y A060229 Cf. A001359, A002110, A060230, A060231, A158277, A158861.
%Y A060229 Subset of A001097, A001359, A132236, A132243 and A132247.
%K A060229 nonn
%O A060229 1,1
%A A060229 _Labos Elemer_, Mar 21 2001
%E A060229 Minor edits by _Ray Chandler_, Apr 02 2009