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
Examples
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.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1001 from Harvey P. Dale)
Programs
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Mathematica
Select[Transpose[Select[Partition[Prime[Range[600]],2,1],#[[2]]-#[[1]]==2&]][[1]],SquareFreeQ[#-1]&] (* Harvey P. Dale, Aug 10 2013 *)
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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) }
Extensions
Offset corrected by Amiram Eldar, Jun 29 2024