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

Author

T. D. Noe, Dec 02 2009

Keywords

• hard
• nonn

Comments

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

Links

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

Crossrefs

Cf. A111287.

Programs

Mathematica

Table[p=Prime[n]; cnt=0; q=2; While[q=NextPrime[q]; If[Mod[q,p]==1, cnt++, cnt=0]; cnt
				

PARI

A168678(n) = {local(p,m,c,r);p=2;r=2;m=prime(n);c=0;while(cMichael B. Porter, Feb 02 2010