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
Keywords
Examples
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.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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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
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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
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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
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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 *) -
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
Formula
a(n) = A078855(n) + 12.
Comments