A217577 - OEIS

%I #8 Oct 08 2012 11:06:03

%S 89,211,359,509,541,691,751,991,1201,1399,1409,1559,1741,2099,2161,

%T 2179,2333,2503,2609,2851,3089,3209,3271,4111,4139,4289,4297,4409,

%U 5309,5591,6151,6389,6397,6491,6599,7283,7411,7993,8039,8101,8467,8609,8941,9391,9661

%N The only prime p such that k*a < p < k*b where a, b are consecutive primes, case k=5.

%C Corresponding values of b-a: 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 6, 4, 4, 2, 2, 2, 2, 6, 2, 2, 2, 4, 2, 2, 6, 2, 2, 4, 4, 2, 6. In most cases b-a = 2. Smallest n for which b-a = 2(2)26: 1, 10, 16, 62, 119, 414, 939, 2565, 1349, 1042, 10470, 22211, 23553.  Also, at n  = 43461,  b-a = 32.

%H Zak Seidov, <a href="/A217577/b217577.txt">Table of n, a(n) for n = 1..10000</a>

%e 89 is the only prime in the interval [5*17, 5*19] = [85,95],

%e 211 is the only prime in the interval [5*41, 5*43] = [205,215],

%e 359 is the only prime in the interval [5*71, 5*73] = [355,365].

%t a = 2; b = 3; s = {}; k = 5; Do[If[(p = NextPrime[k*a]) < k*b && NextPrime[p] > k*b, AppendTo[s, p]]; a = b; b = NextPrime[b], {100}]; s

%Y Cf. A166251 (k=2), A217561 (k=3), A217566 (k=4).

%K nonn

%O 1,1

%A _Zak Seidov_, Oct 07 2012