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A254288 Numbers k such that 4*k + {1, 3, 7, 9, 13, 19} are all prime. 1
1, 370, 41425, 81535, 255625, 267175, 311590, 365350, 1054570, 1381750, 2533600, 2975125, 3266080, 3930205, 4684210, 4782385, 4802860, 5940850, 6414610, 7986565, 8429245, 8570470, 8636305, 8810080, 9270715, 9857980, 10459525, 13708225, 13917490, 15127720, 15252460 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

All terms in this sequence are congruent to 1 mod 3.

Subsequence of A123986.

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..1000 (first 726 terms from K. D. Bajpai)

EXAMPLE

a(2) = 370;

4*370 +  1 = 1481;

4*370 +  3 = 1483;

4*370 +  7 = 1487;

4*370 +  9 = 1489;

4*370 + 13 = 1493;

4*370 + 19 = 1499;

All six are prime.

MATHEMATICA

Select[Range[5*10^7], PrimeQ[4*# + 1] && PrimeQ[4*# + 3] && PrimeQ[4*# + 7] && PrimeQ[4*# + 9] && PrimeQ[4*# + 13] && PrimeQ[4*# + 19] &]

Select[Range[5*10^6], And @@ PrimeQ /@ ({1, 3, 7, 9, 13, 19} + 4 #) &]

PROG

(PARI) for(n=1, 10^7, if( isprime(4*n + 1) && isprime(4*n + 3) &&isprime(4*n + 7) &&isprime(4*n + 9) &&isprime(4*n + 13) &&isprime(4*n + 19) , print1(n, ", ")))

(MAGMA) [n: n in [0..10^8] | forall{4*n+i: i in [1, 3, 7, 9, 13, 19] |  IsPrime(4*n+i)}]; // Vincenzo Librandi, Mar 12 2015

CROSSREFS

Cf. A000040, A005098, A095278, A123986.

Sequence in context: A234985 A264895 A283359 * A281858 A037232 A165330

Adjacent sequences:  A254285 A254286 A254287 * A254289 A254290 A254291

KEYWORD

nonn

AUTHOR

K. D. Bajpai, Jan 27 2015

STATUS

approved

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Last modified August 9 03:33 EDT 2020. Contains 336319 sequences. (Running on oeis4.)