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A217561
The only prime p such that 3a < p < 3b where a, b are consecutive primes.
10
7, 37, 53, 89, 113, 127, 211, 293, 307, 449, 541, 577, 587, 593, 683, 691, 719, 797, 839, 929, 937, 1259, 1297, 1399, 1471, 1499, 1567, 1709, 1777, 1801, 1811, 1847, 1973, 1979, 2039, 2221, 2467, 2503, 2579, 2633, 2647, 2819, 2939, 3037, 3061, 3109, 3187, 3271
OFFSET
1,1
COMMENTS
Corresponding values of b-a: 1, 2, 2, 2, 4, 2, 4, 4, 2, 2, 2, 2, 4, 2, 2, 4, 2, 6, 4, 4, 2, 2, 2, 4, 4, 4, 2, 2, 6, 2, 6, 4, 6, 2, 6, 4, 2, 10. In most cases b-a = 2.
3-isolated primes according to the classification given in the paper on link (see Section 10). - Vladimir Shevelev, Oct 07 2012
LINKS
EXAMPLE
7 is the only prime in the interval [3*2, 3*3] = [6,9],
37 is the only prime in the interval [3*11, 3*13] = [33,39],
53 is the only prime in the interval [3*17, 3*19] = [51,57].
MATHEMATICA
a = 2; b = 3; s = {}; k = 3; Do[If[(p=NextPrime[k*a])< k*b && NextPrime[p] > k*b, AppendTo[s, p]]; a = b; b = NextPrime[b], {100}]; s
NextPrime/@Transpose[Select[3*Partition[Prime[Range[200]], 2, 1], NextPrime[ #[[1]]] == NextPrime[#[[2]], -1]&]][[1]] (* Harvey P. Dale, Oct 12 2012 *)
CROSSREFS
Cf. A166251 (k=2).
Sequence in context: A077720 A235463 A127313 * A003521 A155943 A078626
KEYWORD
nonn
AUTHOR
Zak Seidov, Oct 06 2012
STATUS
approved