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A078848
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 d-pattern=[2,6,4]; short d-string notation of pattern = [264].
16
29, 59, 71, 269, 431, 1289, 2129, 2339, 2381, 2789, 4721, 5519, 5639, 5849, 6569, 6959, 8999, 10091, 13679, 14549, 16649, 16691, 18119, 19379, 19751, 21491, 25931, 27689, 27791, 28619, 31181, 32369, 32561, 32831, 36779, 41609, 43961, 45119
OFFSET
1,1
COMMENTS
Subsequence of A049437. - R. J. Mathar, Feb 10 2013
LINKS
FORMULA
Primes p=p(i) such that p(i+1)=p+2, p(i+2)=p+2+6, p(i+3)=p+2+6+4.
EXAMPLE
29, 29+2=31, 29+2+6=37, 29+2+6+4=41 are consecutive primes.
MATHEMATICA
d = {2, 6, 4}; First /@ Select[Partition[Prime@ Range[10^4], Length@ d + 1, 1], Differences@ # == d &] (* Michael De Vlieger, May 02 2016 *)
Select[Partition[Prime[Range[4700]], 4, 1], Differences[#]=={2, 6, 4}&][[All, 1]] (* Harvey P. Dale, Mar 08 2020 *)
CROSSREFS
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: A033904 A184073 A080170 * A055784 A083821 A042666
KEYWORD
nonn
AUTHOR
Labos Elemer, Dec 11 2002
EXTENSIONS
Listed terms verified by Ray Chandler, Apr 20 2009
Typo in example corrected by Michel Marcus, Dec 28 2013
STATUS
approved