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A217577 The only prime p such that k*a < p < k*b where a, b are consecutive primes, case k=5. 6
89, 211, 359, 509, 541, 691, 751, 991, 1201, 1399, 1409, 1559, 1741, 2099, 2161, 2179, 2333, 2503, 2609, 2851, 3089, 3209, 3271, 4111, 4139, 4289, 4297, 4409, 5309, 5591, 6151, 6389, 6397, 6491, 6599, 7283, 7411, 7993, 8039, 8101, 8467, 8609, 8941, 9391, 9661 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Zak Seidov, Table of n, a(n) for n = 1..10000

EXAMPLE

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

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

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

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A142625 A054694 A132256 * A142826 A251079 A248745

Adjacent sequences:  A217574 A217575 A217576 * A217578 A217579 A217580

KEYWORD

nonn

AUTHOR

Zak Seidov, Oct 07 2012

STATUS

approved

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Last modified June 15 18:33 EDT 2021. Contains 345049 sequences. (Running on oeis4.)