

A052187


Smallest prime p such that p, p+d, and p+2d are consecutive primes for each possible d either 2 or divisible by 6.


6



3, 47, 199, 20183, 16763, 69593, 255767, 247099, 3565931, 6314393, 4911251, 12012677, 23346737, 43607351, 34346203, 36598517, 51041957, 460475467, 652576321, 742585183, 530324329, 807620651, 2988119207, 12447231761, 383204539, 4470607951, 5007182707
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OFFSET

1,1


COMMENTS

The first term 3 is anomalous since for all others d is divisible by 6. These are minimal terms if in A047948 d=6 is replaced by possible differences: (2), 6, 12, 18, ..., 54, 60.
a(54) > 5*10^13, while a(55) = 46186474937633.  Giovanni Resta, Apr 08 2013


LINKS

Donovan Johnson and Giovanni Resta, Table of n, a(n) for n = 1..53 (terms < 5*10^13, first 39 terms from Donovan Johnson)


FORMULA

The least prime(k) such that prime(k+1) = (prime(k) + prime(k+2))/2 and prime(k+1)  prime(k) = d is either 2 or divisible by 6.


EXAMPLE

a(2)=47 and it is the lower border of a dd pattern: 47[6 ]53[6 ]59. a(10)=6314393 and a(10)+54=6314447, a(10)+108=6314501 are consecutive primes and 6314393 is the smallest prime prior to a (54,54) difference pattern of A001223.


MATHEMATICA

a = Table[0, {100}]; NextPrime[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; p = q = r = 0; Do[r = NextPrime[r]; If[r + p == 2q && r  q < 201 && a[[(r  q)/2]] == 0, a[[(r  q)/2]] = p; p = q; q = r, {n, 1, 10^8}]; a (* Typos fixed by Zak Seidov, May 01 2020 *)


CROSSREFS

Cf. A001223, A047948, A052160.
Cf. A052188, A052189, A052195, A052196, A052197, A052198.
Sequence in context: A122535 A058427 A142293 * A260219 A131465 A277388
Adjacent sequences: A052184 A052185 A052186 * A052188 A052189 A052190


KEYWORD

nonn


AUTHOR

Labos Elemer, Jan 28 2000


EXTENSIONS

More terms from Labos Elemer, Jan 04 2002
More terms from Robert G. Wilson v, Jan 06 2002
Definition clarified by Harvey P. Dale, Aug 29 2012
a(23)a(27) from Donovan Johnson, Aug 30 2012


STATUS

approved



