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.

2, 3, 5, 5, 11, 11, 17, 17, 23, 29, 31, 31, 41, 41, 47, 53, 59, 61, 61, 71, 73, 73, 83, 83, 79, 101, 101, 107, 107, 113, 109, 131, 137, 139, 149, 151, 157, 157, 167, 173, 179, 181, 191, 191, 197, 197, 197, 197, 227, 227, 233, 239, 241, 251, 257, 263, 269, 271, 271

Offset

2,1

Comments

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?

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

Links

Michael De Vlieger, Table of n, a(n) for n = 2..10000

Mathematica

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 *)

Prog

(PARI) A152076(n) = local(q=n=prime(n)); while( q=precprime(q-1), issquarefree(n-q) && return(q)) \\ M. F. Hasler, Nov 23 2008

Crossrefs

Cf. A152075, A152073.

Sequence in context: A326187 A071850 A092749 * A133278 A343395 A050368

Adjacent sequences: A152073 A152074 A152075 * A152077 A152078 A152079

Keyword

nonn

Author

Leroy Quet, Nov 23 2008

Extensions

Terms beyond a(13) from M. F. Hasler and Ray Chandler, Nov 23 2008

Status

approved