A108110 - OEIS

%I #11 Dec 23 2024 02:33:46

%S 284,3074,3494,21698,32138,43874,51794,60674,75494,407348,437438,

%T 459794,571478,660878,667358,705464,716624,740774,811028,820154,

%U 910664,1059398,1077998,1122584,1150748,1210754,1222898,1265018,1412174,1461164,1486574,1585868,1631438

%N Numbers n such that prime(k)*n+prime(k+1), for k=1,...,6 all are primes.

%C n == 0 (mod 2). n == 2 (mod 3). n == 3 or 4 (mod 5). - _Jason Yuen_, Sep 02 2024

%e 284 is OK because 2*284+3, 3*284+5, 5*284+7, 7*284+11, 11*284+13 and 13*284+17 all are primes.

%t s={};Do[If[Union[PrimeQ/@Table[Prime[k]*n+Prime[k+1], {k, 6}]]=={True}, s=Append[s, n]], {n, 2, 1000000, 2}];s

%o (PARI) \\ See isok from A108117

%o for(n=1,2*10^6,if(isok(n,6),print1(n", "))) \\ _Jason Yuen_, Sep 02 2024

%Y Cf. A067076 (k=1), A088879 (k=2), A111224 (k=3), A101123 (k=4), A102721 (k=5).

%Y Cf. A108117 (k=1..7), A379427 (k=1..8).

%K nonn

%O 1,1

%A _Zak Seidov_, Jun 03 2005

%E a(22)-a(33) from _Jason Yuen_, Sep 02 2024