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A078856
Initial term in sequence of four consecutive primes whose consecutive differences have d-pattern = [6, 4, 6]; short d-string notation for pattern = [646].
15
73, 157, 373, 433, 1543, 2341, 2383, 3313, 3607, 4441, 4993, 5851, 6037, 6961, 7237, 8731, 9613, 9733, 10723, 13093, 14143, 14731, 16411, 16921, 17971, 18787, 20107, 21391, 23011, 23593, 25111, 25237, 25447, 27793, 30103, 30697, 32353, 32563
OFFSET
1,1
LINKS
FORMULA
Primes p = p_(i) such that p_(i+1) = p + 6, p_(i+2) = p + 6 + 4, p_(i+3) = p + 6 + 4 + 6.
EXAMPLE
p=73, 73 + 6 = 79, 73 + 6 + 4 = 83, 73 + 6 + 4 + 6 = 89 are consecutive primes.
MAPLE
N:=10^4: # to get all terms <= N.
Primes:=select(isprime, [seq(i, i=3..N+16, 2)]):
Primes[select(t->[Primes[t+1]-Primes[t], Primes[t+2]-Primes[t+1],
Primes[t+3]-Primes[t+2]]=[6, 4, 6], [$1..nops(Primes)-3])]; # Muniru A Asiru, Aug 04 2017
MATHEMATICA
Transpose[Select[Partition[Prime[Range[10000]], 4, 1], Differences[#]=={6, 4, 6}&]][[1]] (* Harvey P. Dale, Apr 22 2014 *)
CROSSREFS
Subsequence of A078562.
Cf. analogous prime quadruple sequences with various possible {2, 4, 6}-difference-patterns in brackets: A007530[242], A078847[246], A078848[264], A078849[266], A052378[424], A078850[426], A078851[462], A078852[466], A078853[624], A078854[626], A078855[642], A078856[646], A078857[662], A078858[664], A033451[666].
Sequence in context: A044705 A248399 A071844 * A142326 A142377 A044405
KEYWORD
nonn
AUTHOR
Labos Elemer, Dec 11 2002
EXTENSIONS
Listed terms verified by Ray Chandler, Apr 20 2009
Name simplified by Michel Marcus, Aug 11 2017
STATUS
approved