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A092307
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Primes p such that there are no primes q, 3 < q < p, such that (q-1) divides (p-1).
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10
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5, 7, 11, 23, 47, 59, 83, 107, 167, 179, 227, 239, 263, 347, 359, 383, 443, 467, 479, 503, 563, 587, 647, 659, 719, 827, 839, 863, 887, 983, 1019, 1187, 1223, 1259, 1283, 1307, 1319, 1367, 1439, 1487, 1499, 1523, 1619, 1787, 1823, 1847, 1907, 2027, 2039, 2063
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Using a sieve, these primes can be generated quickly. In the set of primes < 10^9, the density of these primes is about 1/10. It is easy to show that this sequence contains all "safe" primes (A005385).
Primes p such that 6p is the denominator of some Bernoulli number. - T. D. Noe, Sep 26 2006
Except for 5 and 7, primes p such that 12p is the denominator of B(p-1)/(p-1) where B(n) is the Bernoulli number. [From Peter Luschny (peter(AT)luschny.de), Dec 24 2008]
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
P. Luschny, Von Staudt prime number, definiton and computation. [From Peter Luschny (peter(AT)luschny.de), Dec 24 2008]
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FORMULA
| Let h(x)=12x(x+ln(exp(-x)-1)-ln(x)) and [x^n]S(h) denote the coefficient of x^n in the series expansion of h. Consider for n>1 the relation n = denominator((n-1)![x^n]S(h)). [From Peter Luschny (peter(AT)luschny.de), Dec 24 2008]
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MAPLE
| For p>7: seq(`if`(denom(bernoulli(n-1)/(n-1))=12*n, n, NULL), n=2..500); [From Peter Luschny (peter(AT)luschny.de), Dec 24 2008]
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MATHEMATICA
| t=Table[p=Prime[n]; Length[Select[Divisors[p-1]+1, PrimeQ], {n, 150}]; Prime[Flatten[Position[t, 3]]]
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CROSSREFS
| Cf. A090801 (distinct numbers appearing as denominators of Bernoulli numbers)
Cf. A092308 (for p=prime(n), the number of primes q such that q-1 divides p-1).
Cf. A005385 (primes p such that (p-1)/2 is also prime).
Cf. A152951. [From Peter Luschny (peter(AT)luschny.de), Dec 24 2008]
Sequence in context: A124111 A151715 A090810 * A005385 A181602 A075705
Adjacent sequences: A092304 A092305 A092306 * A092308 A092309 A092310
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Feb 12 2004
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