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A316630 Numbers k such that 10k+1, 10k+3, 10k+7, and 10k+9 are all composite, and k == 1 (mod 3). 1
133, 196, 232, 256, 298, 328, 397, 403, 406, 418, 430, 457, 484, 640, 643, 664, 709, 727, 742, 802, 847, 865, 898, 907, 970, 991, 1012, 1054, 1057, 1081, 1087, 1096, 1120, 1153, 1156, 1213, 1231, 1246, 1327, 1354, 1360, 1381, 1411, 1423, 1426, 1435, 1480, 1504 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The sequence contains all numbers of the form 50151*m + 42175. - Michael B. Porter, Jul 16 2018

If m is in the sequence, then so is m + 3*(10*m+1)*(10*m+3)*(10*m+7)*(10*m+9)*k for all k. - Robert Israel, Aug 08 2018

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

C. K. Caldwell, The Prime Pages Top Twenty: Quadruplet, list of largest known prime quadruplets.

EXAMPLE

1331 = 11^3, 1333 = 31*43, 1337 = 7*191, 1339 = 13*103, and 133 == 1 (mod 3), so 133 is a sequence member.

MAPLE

remove(t -> ormap(isprime, [10*t+1, 10*t+3, 10*t+7, 10*t+9]), [seq(k, k=1..2000, 3)]); # Robert Israel, Aug 08 2018

MATHEMATICA

Select[1 + 3 Range@510, Union[ PrimeQ[10 # + {1, 3, 7, 9}]] == {False} &] (* Robert G. Wilson v, Jul 16 2018 *)

PROG

(PARI) ok(k)={if(k%3==1, for(i=0, 4, if(isprime(10*k+2*i+1), return(0))); 1, 0)} \\ Andrew Howroyd, Jul 10 2018

(MATLAB) m=1; for s=1:510 v=[30*s+11, 30*s+13, 30*s+17, 30*s+19]; if isprime(v)==0  sol(m)=3*s+1; m=m+1; end; end; sol % Marius A. Burtea, Sep 17 2019

(MAGMA) [3*s+1: s in [0..510] | forall{30*s+k: k in [11, 13, 17, 19] | not IsPrime(30*s+k)}]; // Marius A. Burtea, Sep 17 2019

CROSSREFS

Cf. A007811, A032352.

Sequence in context: A102619 A020446 A123997 * A250766 A254692 A050882

Adjacent sequences:  A316627 A316628 A316629 * A316631 A316632 A316633

KEYWORD

nonn,easy

AUTHOR

Patrick A. Thomas, Jul 09 2018

STATUS

approved

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Last modified August 10 03:18 EDT 2022. Contains 356029 sequences. (Running on oeis4.)