A209617 -id:A209617 - cp's OEIS frontend

A209624 Primes separated from their previous adjacent primes by a prime number of successive composites.

11, 17, 23, 29, 37, 41, 47, 53, 59, 67, 71, 79, 83, 89, 97, 101, 107, 113, 127, 131, 137, 157, 163, 167, 173, 179, 197, 211, 223, 227, 233, 239, 257, 263, 269, 277, 281, 307, 311, 317, 331, 337, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 439, 443, 449

Offset: 1

Lekraj Beedassy, Mar 10 2012

nonn

			a(1)=11 is the first prime separated from the previous prime (7) by a prime number (3) of successive composites, namely, 10, 9, 8.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A209617.

Select[Prime[Range[2, 100]], PrimeQ[# - NextPrime[#, -1] - 1] &] (* T. D. Noe, Mar 12 2012 *)
Select[Partition[Prime[Range[100]],2,1],PrimeQ[#[[2]]-#[[1]]-1]&][[All,2]] (* Harvey P. Dale, Jul 14 2020 *)

a(n) = A151800(A209617).

A272367 Primes p separated from their adjacent primes on both sides by a prime number of successive composites, while the adjacent primes of p are separated by a prime number of integers.

Original entry on oeis.org

53, 89, 97, 113, 127, 157, 173, 211, 257, 263, 307, 317, 331, 359, 367, 373, 389, 397, 401, 449, 457, 479, 487, 491, 499, 509, 541, 563, 593, 607, 653, 683, 727, 733, 743, 751, 761, 769, 773, 853, 863, 877, 887, 907, 911, 937, 947, 953, 967, 977, 983, 991, 997, 1069, 1103, 1109, 1117, 1123, 1187

Offset: 1

Marc Morgenegg, Apr 27 2016

nonn

			a(1) = 53. The primes around and including 53 are {47, 53, 59}. The number of composites between these are {5, 5} and the number of integers between 47 and 59 is 11; all of {5, 5, 11} are prime, thus 53 is a term.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Subsequence of A209617.

Select[Prime@ Range@ 195, Function[p, Times @@ Boole@ PrimeQ@ Flatten[Map[Differences, {#, Delete[#, 2]}] - 1] &@ Map[NextPrime[p, #] &, Range[-1, 1]] == 1]] (* Michael De Vlieger, Apr 27 2016 *)

list(lim)=my(v=List(),p=2,q=3); forprime(r=5,nextprime(lim\1+1), if(isprime(q-p-1) && isprime(r-q-1) && isprime(r-p-1), listput(v,q)); p=q; q=r); Vec(v) \\ Charles R Greathouse IV, Apr 30 2016

More terms from Michael De Vlieger, Apr 27 2016

cp's OEIS Frontend

A209624 Primes separated from their previous adjacent primes by a prime number of successive composites.

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