%I #36 Sep 08 2022 08:45:03

%S 29,59,149,179,239,269,419,569,599,659,809,1019,1049,1229,1289,1319,

%T 1619,1949,2129,2309,2339,2549,2729,2789,2969,2999,3119,3299,3329,

%U 3359,3389,3539,3929,4019,4049,4229,4259,4649,4799,5009,5099,5279,5519,5639

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

%C Equivalently, smaller of twin prime pair with primes in different decades.

%C 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 The union of this sequence and A282326 gives A132243. - _Martin Renner_, Feb 11 2017

%C The union of {3,5}, A282321, A282323 and this sequence gives A001359. - _Martin Renner_, Feb 11 2017

%C The union of {3,5,7}, A282321, A282322, A282323, A282324, this sequence and A282326 gives A001097. - _Martin Renner_, Feb 11 2017

%C 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 Muniru A Asiru, <a href="/A060229/b060229.txt">Table of n, a(n) for n = 1..1000</a>

%e For the pair {149,151} (149 + 151)/2 = 5*30.

%p isA060229 := proc(n)

%p if modp(n+1,30) =0 and isprime(n) and isprime(n+2) then

%p true;

%p else

%p false;

%p end if;

%p end proc:

%p A060229 := proc(n)

%p option remember;

%p if n =1 then

%p 29;

%p else

%p for a from procname(n-1)+2 by 2 do

%p if isA060229(a) then

%p return a;

%p end if;

%p end do:

%p end if;

%p end proc:

%p seq(A060229(n),n=1..80) ; # _R. J. Mathar_, Feb 19 2017

%t Select[Prime@ Range[10^3], PrimeQ[# + 2] && Mod[# + 1, 30] == 0 &] (* _Michael De Vlieger_, Jul 14 2016 *)

%o (PARI) isok(n) = isprime(n) && isprime(n+2) && !((n+1) % 30); \\ _Michel Marcus_, Dec 11 2013

%o (Magma) [p: p in PrimesUpTo(7000) | IsPrime(p+2) and p mod 30 eq 29 ]; // _Vincenzo Librandi_, Feb 13 2017

%o (GAP) Filtered(List([0..200], k -> 30*k-1), n -> IsPrime(n) and IsPrime(n+2)); # _Muniru A Asiru_, Feb 02 2018

%Y Cf. A001359, A002110, A060230, A060231, A158277, A158861.

%Y Subset of A001097, A001359, A132236, A132243 and A132247.

%K nonn

%O 1,1

%A _Labos Elemer_, Mar 21 2001

%E Minor edits by _Ray Chandler_, Apr 02 2009