A284659 Numbers n such that numbers 30(n+k) + 1 are prime for k=0..5.

18, 74, 4386, 4505, 9314, 10357, 21095, 29621, 38784, 102463, 105200, 116134, 163300, 179967, 186918, 210515, 252830, 348709, 354022, 362345, 396820, 400915, 431568, 438862, 457748, 464118, 470852, 477341, 493070

Offset: 1

Author

Zak Seidov, Mar 31 2017

Keywords

• nonn

Comments

Numbers n through n+5 are terms in A111175. There are no cases of 7 consecutive numbers in A111175.

All terms are congruent to 4 mod 7.

Examples

			a(1)=18 because 1 + 30*k for k=18..23 are 541, 571, 601, 631, 661, 691 all primes: A000040(k) for k={100, 105, 110, 115, 121, 125}.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000
• Index entries for primes in AP

Crossrefs

Cf. A111175, A132230.

Programs

Maple

filter:= t -> andmap(isprime, [seq(30*(t+k)+1, k=0..5)]):
select(filter, [seq(seq(77*k + i,i=[18,39,53,60,74]),k=0..10000)]); # Robert Israel, Apr 04 2017

Mathematica

Select[Range[18, 1000000, 7], PrimeQ[1 + 30*#] && PrimeQ[1 + 30*(# + 1)] && PrimeQ[1 + 30*(# + 2)] && PrimeQ[1 + 30*(# + 3)] && PrimeQ[1 + 30*(# + 4)] && PrimeQ[1 + 30*(# + 5)] &]
Select[Range[4,10^6,7],AllTrue[30(#+Range[0,5])+1,PrimeQ]&] (* Harvey P. Dale, Dec 03 2023 *)