A284101 Initial primes of 14 consecutive primes all congruent to 5 mod 6.

19725473, 19725479, 40727657, 40962983, 40962989, 44291297, 45404537, 45404543, 54470123, 54470147, 63846089, 63846119, 68208599, 68208611, 68364221, 90007661, 93602507, 99492971, 99492977, 99579647, 99579671, 117585977, 117585983

Offset: 1

Author

Zak Seidov, Mar 20 2017

Keywords

• nonn

Comments

Prime indices of a(n): 1254203,1254204,2475221,2488622,2488623,2677942,2741244,2741245.

a(1) = 19725473 = A057622(14). Actually 19725473, 40962983 and 45404537 are the initial primes of 15 such consecutive primes that is also a(1) = A057622(15).

Examples

			15 consecutive primes starting with 19725473 are
{19725473, 19725479, 19725527, 19725533, 19725599, 19725617, 19725623, 19725653, 19725659, 19725677, 19725683, 19725689, 19725701, 19725731, 19725737} with gaps
{6, 48, 6, 66, 18, 6, 30, 6, 18, 6, 6, 12, 30, 6} - all multiples of 6.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A057622 Initial prime in first sequence of n consecutive primes all congruent to 5 mod 6.

Programs

Mathematica

Select[Partition[Prime[Range[68*10^5]],14,1],AllTrue[Mod[#,6]==5&]][[;;,1]] (* Harvey P. Dale, Mar 06 2023 *)
Prime[#]&/@(SequencePosition[If[Mod[#,6]==5,1,0]&/@Prime[Range[672*10^4]],PadRight[{},14,1]][[;;,1]]) (* Harvey P. Dale, Sep 22 2024 *)

PARI

list(lim)=my(v=List(), P=primes(14), goal=vector(14,i,5), pm=P%6, idx=1); forprime(p=P[#P]+1,, P[idx]=p; pm[idx]=p%6; if(idx++>14,idx=1); if(P[idx]>lim, break); if(pm==goal, listput(v, P[idx]))); Vec(v) \\ Charles R Greathouse IV, Mar 20 2017

Extensions

a(9)-a(23) from Charles R Greathouse IV, Mar 20 2017