cp's OEIS Frontend

A152076 a(n) = the largest prime p < prime(n) such that prime(n) - p is squarefree, where prime(n) is the n-th prime. a(n) = 0 if no such prime p exists.

%I A152076 #18 Sep 05 2019 10:41:48
%S A152076 2,3,5,5,11,11,17,17,23,29,31,31,41,41,47,53,59,61,61,71,73,73,83,83,
%T A152076 79,101,101,107,107,113,109,131,137,139,149,151,157,157,167,173,179,
%U A152076 181,191,191,197,197,197,197,227,227,233,239,241,251,257,263,269,271,271
%N A152076 a(n) = the largest prime p < prime(n) such that prime(n) - p is squarefree, where prime(n) is the n-th prime. a(n) = 0 if no such prime p exists.
%C A152076 Does every odd prime differ from some smaller prime by a squarefree integer? Or is there at least one term of this sequence equal to 0?
%C A152076 Indices for which a(n)<a(n-1) are n = 26, 32, 64, 79, 89, 92, 98, 100, 123, 127, 129, 133, 136, 148, 152, 159, 164, 169, 181, 193,... - _M. F. Hasler_, Nov 23 2008
%H A152076 Michael De Vlieger, <a href="/A152076/b152076.txt">Table of n, a(n) for n = 2..10000</a>
%t A152076 Table[NestWhile[NextPrime[#, -1] &, p, ! SquareFreeQ[# - p] &], {p, Prime@ Range[2, 10^4]}] (* _Michael De Vlieger_, Oct 30 2017, after _Harvey P. Dale_ at A152075 *)
%o A152076 (PARI) A152076(n) = local(q=n=prime(n)); while( q=precprime(q-1), issquarefree(n-q) && return(q)) \\ _M. F. Hasler_, Nov 23 2008
%Y A152076 Cf. A152075, A152073.
%K A152076 nonn
%O A152076 2,1
%A A152076 _Leroy Quet_, Nov 23 2008
%E A152076 Terms beyond a(13) from _M. F. Hasler_ and _Ray Chandler_, Nov 23 2008