A290635 Greatest of 4 consecutive primes with consecutive gaps 6, 4, 2.

43, 73, 283, 619, 1303, 1669, 1789, 1873, 1999, 2143, 2383, 2689, 2803, 4519, 5419, 5443, 5653, 7879, 9013, 11833, 13693, 14563, 17389, 18133, 18313, 20359, 21493, 22159, 24109, 27283, 32719, 35533, 36793, 37573, 41233, 41959, 42409, 42463, 44269, 47149, 50593, 55219, 55819, 55933

Offset

1,1

Comments

All terms = {13, 19} mod 30.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = A078855(n) + 12.

Example

43 is a member of the sequence because 43 is the greatest of the 4 consecutive primes 31, 37, 41, 43 with consecutive gaps 6, 4, 2; that is, 37 - 31 = 6, 41 - 37 = 4, 43 - 41 = 2.

Maple

for i from 1 to 10^5 do if ithprime(i+1)=ithprime(i)+6 and ithprime(i+2)=ithprime(i)+4 and ithprime(i+3)=ithprime(i)+2  then print(ithprime(i+3)); fi; od; # Corrected by Robert Israel, Jun 28 2018
# More efficient:
primes:= select(isprime, [seq(seq(30*i+j, j=[13, 19]), i=1..10^4)]):
select(t -> isprime(t-2) and isprime(t-6) and isprime(t-12) and not isprime(t-8), primes); # Robert Israel, Jun 28 2018

Mathematica

With[{s = Differences@ Prime@ Range[10^4]}, Prime[1 + SequencePosition[s, {6, 4, 2}][[All, -1]] ] ] (* Michael De Vlieger, Aug 16 2017 *)
Select[Partition[Prime[Range[6000]], 4, 1], Differences[#]=={6, 4, 2}&][[All, 4]] (* Harvey P. Dale, Feb 13 2022 *)

Prog

(GAP)
K:=2*10^5+1;; # to get all terms <= K.
P:=Filtered([1, 3..K], IsPrime);;  I:=Reversed([2, 4, 6]);;
P1:=List([1..Length(P)-1], i->P[i+1]-P[i]);;
P2:=List([1..Length(P)-Length(I)], i->[P1[i], P1[i+1], P1[i+2]]);;
P3:=List(Positions(P2, I), i->P[i+Length(I)]);
# More efficient
(GAP) Filtered(Set(Flat(List([13, 19], j->List([1..2000], i->30*i+j)))), j->IsPrime(j) and IsPrime(j-12) and not IsPrime(j-10) and not IsPrime(j-8) and IsPrime(j-6) and not IsPrime(j-4) and IsPrime(j-2)); # Muniru A Asiru, Jul 03 2018
(PARI) is(n) = if(!ispseudoprime(n), return(0), my(v=[n-2, n-6, n-12]); if(v[1]==precprime(n-1) && v[2]==precprime(v[1]-1) && v[3]==precprime(v[2]-1), return(1))); 0 \\ Felix Fröhlich, Aug 10 2017

Crossrefs

Subsequence of A006512 and A098413.

Cf. A022005, A078855.

Sequence in context: A054807 A285017 A139932 * A176925 A080177 A238248

Adjacent sequences: A290632 A290633 A290634 * A290636 A290637 A290638

Keyword

nonn

Author

Muniru A Asiru, Aug 08 2017

Status

approved