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

1,1

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).

Links

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

Example

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.

Mathematica

Select[Partition[Prime[Range[68*10^5]], 14, 1], AllTrue[Mod[#, 6]==5&]][[;; , 1]] (* Harvey P. Dale, Mar 06 2023 *)

Prog

(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

Crossrefs

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

Sequence in context: A348267 A172767 A122557 * A303448 A251513 A103123

Adjacent sequences: A284098 A284099 A284100 * A284102 A284103 A284104

Keyword

nonn

Author

Zak Seidov, Mar 20 2017

Extensions

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

Status

approved