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A055781 Primes q of the form q = 10p + 1, where p is also prime. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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]

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

1031 = 103*10 + 1, 1 appended to 103.

MAPLE

select(isprime, map(t-> 10*t+1, select(isprime, [3, seq(i, i=7..2000, 6)]))); # Robert Israel, Jun 13 2017

MATHEMATICA

Select[10Prime[Range[200]]+1, PrimeQ]  (* Harvey P. Dale, Feb 04 2011 *)

PROG

(PARI) is(n)=n%10==1 && isprime(n) && isprime(n\10) \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A005384, A005385, A023237.

Sequence in context: A304292 A127191 A003542 * A142195 A237992 A139975

Adjacent sequences:  A055778 A055779 A055780 * A055782 A055783 A055784

KEYWORD

nonn

AUTHOR

Labos Elemer, Jul 13 2000

STATUS

approved

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Last modified October 18 02:23 EDT 2019. Contains 328135 sequences. (Running on oeis4.)