

A078851


Initial term in sequence of four consecutive primes separated by 3 consecutive differences each <=6 (i.e., when d=2,4 or 6) and forming dpattern=[4, 6, 2]; short dstring notation of pattern = [462].


16



19, 127, 229, 1009, 1279, 1597, 1609, 2539, 3319, 3529, 3907, 3919, 4639, 4789, 4999, 5839, 5857, 7477, 7537, 8419, 9619, 12097, 12907, 13327, 15259, 15877, 17569, 17977, 19069, 22027, 23017, 24967, 27739, 28537, 32359, 33577, 36919, 38317
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OFFSET

1,1


COMMENTS

Subsequence of A078561.  R. J. Mathar, May 06 2017


LINKS

R. J. Mathar, Table of n, a(n) for n = 1..1000


FORMULA

Primes p = p(i) such that p(i+1)=p+4, p(i+2)=p+4+6, p(i+3)=p+4+6+2.


EXAMPLE

p=19,19+4=23,19+4+6=29,19+4+6+2=31 are consecutive primes.


MATHEMATICA

Select[Prime@ Range[10^4], Differences@ Prime@ Range[#, # + 3] &@ PrimePi@ # == {4, 6, 2} &] (* Michael De Vlieger, Jul 02 2016 *)


CROSSREFS

Cf. analogous prime quadruple sequences with various possible {2, 4, 6}differencepatterns 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: A109669 A164905 A142106 * A202125 A169727 A177459
Adjacent sequences: A078848 A078849 A078850 * A078852 A078853 A078854


KEYWORD

nonn


AUTHOR

Labos Elemer, Dec 11 2002


EXTENSIONS

Listed terms verified by Ray Chandler, Apr 20 2009


STATUS

approved



