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A108110
Numbers n such that prime(k)*n+prime(k+1), for k=1,...,6 all are primes.
1
284, 3074, 3494, 21698, 32138, 43874, 51794, 60674, 75494, 407348, 437438, 459794, 571478, 660878, 667358, 705464, 716624, 740774, 811028, 820154, 910664, 1059398, 1077998, 1122584, 1150748, 1210754, 1222898, 1265018, 1412174, 1461164, 1486574, 1585868, 1631438
OFFSET
1,1
COMMENTS
n == 0 (mod 2). n == 2 (mod 3). n == 3 or 4 (mod 5). - Jason Yuen, Sep 02 2024
EXAMPLE
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.
MATHEMATICA
s={}; Do[If[Union[PrimeQ/@Table[Prime[k]*n+Prime[k+1], {k, 6}]]=={True}, s=Append[s, n]], {n, 2, 1000000, 2}]; s
PROG
(PARI) \\ See isok from A108117
for(n=1, 2*10^6, if(isok(n, 6), print1(n", "))) \\ Jason Yuen, Sep 02 2024
CROSSREFS
Cf. A067076 (k=1), A088879 (k=2), A111224 (k=3), A101123 (k=4), A102721 (k=5).
Cf. A108117 (k=1..7).
Sequence in context: A343917 A143191 A180220 * A218400 A196893 A280808
KEYWORD
nonn
AUTHOR
Zak Seidov, Jun 03 2005
EXTENSIONS
a(22)-a(33) from Jason Yuen, Sep 02 2024
STATUS
approved