A173088 - OEIS

%I #13 Sep 08 2022 08:45:50

%S 2,5,7,12,18,25,33,40,47,72,95,138,170,172,177,215,242,278,333,347,

%T 352,373,385,443,495,550,555,560,588,637,670,688,705,707,753,975,1045,

%U 1110,1127,1243,1260,1433,1495,1502,1572,1668,1673,1712,1717,1738,1750,1810

%N Numbers k such that 6*k - 1, 6*k + 1, 6*k + 29, and 6*k + 31 are primes.

%C Numbers n such that n and n+5 are both in A002822.

%H Amiram Eldar, <a href="/A173088/b173088.txt">Table of n, a(n) for n = 1..10000</a>

%e A002822 starts 1,2,3,5,7,10,12,17,18,23,... Hence the first terms are 2 (7 is in A002822), 5 (10 is in A002822), 7 (12 is in A002822), 12 (17 is in A002822), 18 (23 is in A002822).

%p # From _R. J. Mathar_, Mar 01 2010: (Start)

%p isA002822 := proc(n)

%p if isprime(6*n-1) and isprime(6*n+1) then

%p true;

%p else

%p false;

%p end if;

%p end proc:

%p isA173088 := proc(n)

%p isA002822(n) and isA002822(n+5) ;

%p end proc:

%p for n from 1 to 1700 do

%p if isA173088(n) then

%p printf("%d,",n) ;

%p end if;

%p end do ; # (End)

%t Select[Range[2000], And @@ PrimeQ[6*# + {-1, 1, 29, 31}] &] (* _Amiram Eldar_, Jan 01 2020 *)

%o (Magma) A002822:=[ k: k in [1..3000] | IsPrime(6*k-1) and IsPrime(6*k+1) ]; [ p: p in A002822 | p+5 in A002822 ]; // _Klaus Brockhaus_, Mar 01 2010

%Y Cf. A002822 (numbers n such that 6*n-1, 6*n+1 are twin primes).

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Feb 14 2010

%E Edited, corrected and extended by _Klaus Brockhaus_, _R. J. Mathar_ and _N. J. A. Sloane_, Mar 03 2010

%E Edited by _Charles R Greathouse IV_, Mar 24 2010