A141831 - OEIS

%I #8 Oct 04 2015 01:44:19

%S 7,19,23,31,43,47,53,67,73,79,83,89,103,113,127,131,139,151,157,163,

%T 167,173,181,199,211,223,233,241,251,257,263,271,283,293,307,317,331,

%U 337,353,359,367,373,379,383,389,401,409,421,433,439,443,449,463,467,479

%N Primes not in sequence A141830.

%C This sequence gives the primes p where not every positive integer k <= q-p divides p-1, where q is the prime immediately after p.

%p isA141831 := proc(p) local q,d ; if isprime(p) then q := nextprime(p) ; for d from 1 to q-p do if (p+d-1) mod d <> 0 then RETURN(true) ; fi; od: RETURN(false) ; else false; fi; end: for i from 1 to 300 do p := ithprime(i) ; if isA141831(p) then printf("%d,",p) ; fi; od: # _R. J. Mathar_, Aug 08 2008

%t fQ[n_] := Block[{p = n, q = NextPrime@ n}, Union[IntegerQ /@ (Range[p, q - 1]/Range[q - p])][[1]]]; Select[ Prime@ Range@ 92, !fQ@ # &] (* _Robert G. Wilson v_ *)

%Y Cf. A141829, A141830.

%K nonn

%O 1,1

%A _Leroy Quet_, Jul 09 2008

%E Extended beyond 53 by _R. J. Mathar_, Aug 08 2008