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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 26 09:15 EDT 2021. Contains 347664 sequences. (Running on oeis4.)