A168678 Least prime p such that the prime(n)-1 consecutive primes starting at p are all congruent to 1 (mod prime(n)).

3, 31, 22501, 9984437

Offset

1,1

Comments

By a theorem of Shiu, a(n) exists for all n.

Links

Table of n, a(n) for n=1..4.

D. K. L. Shiu, Strings of Congruent Primes, J. Lond. Math. Soc. 61 (2) (2000) 359-373 [MR1760689]

Mathematica

Table[p=Prime[n]; cnt=0; q=2; While[q=NextPrime[q]; If[Mod[q, p]==1, cnt++, cnt=0]; cnt<p-1]; If[p==2, q, NextPrime[q, -p+2]], {n, 4}]

Prog

(PARI) A168678(n) = {local(p, m, c, r); p=2; r=2; m=prime(n); c=0; while(c<m-1, if(p%m==1, c++, c=0; r=nextprime(p+1)); p=nextprime(p+1)); r} \\ Michael B. Porter, Feb 02 2010

Crossrefs

Cf. A111287.

Sequence in context: A283247 A261472 A144964 * A276199 A118913 A297480

Adjacent sequences: A168675 A168676 A168677 * A168679 A168680 A168681

Keyword

hard,nonn

Author

T. D. Noe, Dec 02 2009

Status

approved