A141830 - OEIS

%I #11 Mar 20 2015 19:17:26

%S 2,3,5,11,13,17,29,37,41,59,61,71,97,101,107,109,137,149,179,191,193,

%T 197,227,229,239,269,277,281,311,313,347,349,397,419,431,457,461,521,

%U 541,569,599,601,613,617,641,659,673,757,769,809,821,827,853,857,877

%N Primes p such that 1|p, 2|(p+1), 3|(p+2), 4|(p+3),...,(q-p)|(q-1), where q is the prime immediately after p.

%C This sequence also gives the primes p such that every positive integer k <= q-p divides p-1, where q is the prime immediately after p.

%C Number of terms less than 10^k: 3, 13, 57, 338, 2020, 13569, 98365, 736332, 5729411, ..., . Compare these to A006880. - _Robert G. Wilson v_, Aug 01 2008

%H Robert G. Wilson v, <a href="/A141830/b141830.txt">Table of n, for n = 1..13569</a>.

%p isA141830 := 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(false) ; fi; od: RETURN(true) ; else false; fi; end: for i from 1 to 300 do p := ithprime(i) ; if isA141830(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@ 151, fQ@# &] (* _Robert G. Wilson v_ *)

%Y Cf. A141829, A141831.

%K nonn

%O 1,1

%A _Leroy Quet_, Jul 09 2008

%E More terms from _Robert G. Wilson v_ and _R. J. Mathar_, Aug 08 2008