A152076 -id:A152076 - cp's OEIS frontend

A152075 a(n) = the smallest prime p > prime(n) such that p - prime(n) is squarefree, where prime(n) is the n-th prime.

3, 5, 7, 13, 13, 19, 19, 29, 29, 31, 37, 43, 43, 53, 53, 59, 61, 67, 73, 73, 79, 89, 89, 103, 103, 103, 109, 109, 131, 127, 137, 137, 139, 149, 151, 157, 163, 173, 173, 179, 181, 191, 193, 199, 199, 229, 233, 229, 229, 239, 239, 241, 251, 257, 263, 269, 271, 277

Offset: 1

Leroy Quet, Nov 23 2008

nonn

Indices for which a(n)M. F. Hasler, Nov 23 2008

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A152076.

nxtp[n_]:=NestWhile[NextPrime[#]&,n,!SquareFreeQ[#-n]&]; nxtp/@Prime[Range[60]]  (* Harvey P. Dale, Apr 23 2011 *)

A152075(n)=local( p=prime(n), q=p); until( issquarefree(q-p), q=nextprime(q+1)); q \\ M. F. Hasler, Nov 23 2008

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

A152073 a(n) = largest prime < prime(n) such that prime(n) - a(n) is a power of 2, where prime(n) is the n-th prime; a(n) = 0 if no such prime exists.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 13, 29, 29, 37, 41, 43, 37, 43, 59, 59, 67, 71, 71, 79, 73, 89, 97, 101, 103, 107, 109, 0, 127, 73, 137, 0, 149, 149, 131, 163, 157, 163, 179, 127, 191, 193, 197, 179, 191, 223, 227, 229, 223, 239, 0, 241, 199, 13, 269, 269, 277, 281, 277, 179

Offset: 2

Leroy Quet, Nov 23 2008

a(n) = 0 for odd primes prime(n) appearing in A065381.

Primes p(n) for which there is no such prime a(n) (in which case a(n)=0) are listed in A065381 = (2,127,149,251,331,337,373,...). - M. F. Hasler, Nov 23 2008

			Looking at the primes less than the 10th prime = 29: 29 - 23 = 6, not a power of 2. 29-19 = 10, not a power of 2. 29-17 = 12, not a power of 2. But 29-13 = 16, a power of 2. Since p = 13 is the largest prime p such that 29 - p = a power of 2, then a(10) = 13.

Ivan Neretin, Table of n, a(n) for n = 2..10000

Cf. A065381, A139758, A152075, A152076, A156695.

Table[Max[0, Select[# - 2^Range[0, Log2@#] &@Prime[n], PrimeQ]], {n, 2, 63}] (* Ivan Neretin, Jun 10 2018 *)

A152073(n)=local( q=n=prime(n)); while( q=precprime(q-1), n-q==1<M. F. Hasler, Nov 23 2008

Edited and extended by M. F. Hasler and Ray Chandler, Nov 23 2008

cp's OEIS Frontend

A152075 a(n) = the smallest prime p > prime(n) such that p - prime(n) is squarefree, where prime(n) is the n-th prime.

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