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A055781
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Primes q of the form q = 10p + 1, where p is also prime.
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7
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31, 71, 131, 191, 311, 431, 971, 1031, 1091, 1511, 1571, 1811, 1931, 2111, 2411, 2711, 3371, 3491, 3671, 4091, 4211, 4391, 4871, 5231, 5471, 5711, 6011, 6131, 6311, 6911, 7331, 7691, 8111, 8231, 8291, 8831, 9371, 10091, 10211, 10331, 10391, 10631
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OFFSET
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1,1
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COMMENTS
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Corresponding values of p in A023237. - Jaroslav Krizek, Jul 14 2010
From Sergey Pavlov, Jun 14 2017: (Start)
Let a, b, and c be prime numbers such that c = 10b + 1 = 10 * (10a + 1) + 1. Then c = 311, b = 31, a = 3. (There are no other solutions since any prime p > 3 is either of the form 3k + 1 or 3k - 1. In other words, while a > 3 and a, b are primes, a == 1 (mod 3), b == -1 (mod 3), whereas c == 0 (mod 3).)
So is for any similar sequence of primes (of the form kn + 1) where 2k + 1 == 0 (mod 3), e.g., for A002144: the equation of the form c = kb + 1 = k * (ka + 1) + 1 while a, b, c are primes could have the only solution iff a = 3 (but also could have not).
(End) [This comment needs to be rewritten. - N. J. A. Sloane, Feb 18 2019]
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..10000
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EXAMPLE
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1031 = 103*10 + 1, 1 appended to 103.
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MAPLE
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select(isprime, map(t-> 10*t+1, select(isprime, [3, seq(i, i=7..2000, 6)]))); # Robert Israel, Jun 13 2017
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MATHEMATICA
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Select[10Prime[Range[200]]+1, PrimeQ] (* Harvey P. Dale, Feb 04 2011 *)
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PROG
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(PARI) is(n)=n%10==1 && isprime(n) && isprime(n\10) \\ Charles R Greathouse IV, Jun 17 2017
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CROSSREFS
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Cf. A005384, A005385, A023237.
Sequence in context: A304292 A127191 A003542 * A142195 A237992 A139975
Adjacent sequences: A055778 A055779 A055780 * A055782 A055783 A055784
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KEYWORD
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nonn
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AUTHOR
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Labos Elemer, Jul 13 2000
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STATUS
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approved
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