A108110 - OEIS

A108110

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

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

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OFFSET

1,1

COMMENTS

n == 0 (mod 2). n == 2 (mod 3). n == 3 or 4 (mod 5). - Jason Yuen, Sep 02 2024

LINKS

Table of n, a(n) for n=1..33.

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

Adjacent sequences: A108107 A108108 A108109 * A108111 A108112 A108113

KEYWORD

nonn

AUTHOR

Zak Seidov, Jun 03 2005

EXTENSIONS

a(22)-a(33) from Jason Yuen, Sep 02 2024

STATUS

approved