A089188 Lesser member p of a pair of twin primes such that p-1 is squarefree.

3, 11, 59, 71, 107, 179, 191, 227, 239, 311, 347, 419, 431, 599, 659, 827, 1019, 1031, 1091, 1319, 1427, 1487, 1607, 1619, 1787, 1871, 1931, 2027, 2087, 2111, 2267, 2339, 2591, 2687, 2711, 2999, 3119, 3167, 3299, 3359, 3371, 3467, 3527, 3539, 3671, 3767

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1001 from Harvey P. Dale)

Example

71 is a term because it is a prime, 71 + 2 = 73 is a prime, and 71 - 1 = 70 = 2 * 5 * 7 is squarefree.
17 is not a term because 17 - 1 = 2^4.

Mathematica

Select[Transpose[Select[Partition[Prime[Range[600]], 2, 1], #[[2]]-#[[1]]==2&]][[1]], SquareFreeQ[#-1]&] (* Harvey P. Dale, Aug 10 2013 *)

Prog

(PARI) pm1th(n) = { c=0; pc=0; forprime(x=2, n, pc++; y=x-1; if(isprime(x+2), if(issquarefree(y), c++; print1(x", "); ) ) ); print(); print(c", "pc", "c/pc+.0) }

Crossrefs

Intersection of A001359 and A039787.

Cf. A005117.

Sequence in context: A168325 A141776 A071698 * A086827 A308487 A164291

Adjacent sequences: A089185 A089186 A089187 * A089189 A089190 A089191

Keyword

easy,nonn

Author

Cino Hilliard, Dec 07 2003

Extensions

Offset corrected by Amiram Eldar, Jun 29 2024

Status

approved