A075570 Lexicographically earliest sequence of distinct composite numbers such that a(k) + a(k+1) is prime for all k.

4, 9, 8, 15, 14, 27, 10, 21, 16, 25, 6, 35, 12, 49, 18, 55, 24, 65, 32, 39, 20, 33, 26, 45, 22, 51, 28, 69, 34, 63, 38, 75, 52, 57, 40, 87, 44, 93, 46, 81, 50, 77, 30, 119, 48, 91, 36, 95, 42, 85, 54, 125, 56, 111, 62, 105, 58, 99, 64, 115, 66, 133, 60, 121, 70, 123, 68, 129, 82

Offset

1,1

Comments

Index of composite values: {1, 4, 3, 8, 7, 17, 5, 12, 9, 15, 2, 23, 6, 33, 10, 38, 14, 46, 20, 26, 11, 21, 16, 30, ...}. - Michael De Vlieger, Jul 18 2017

Links

Michael De Vlieger, Table of n, a(n) for n = 1..3000

Maple

P:=proc(q) local a, k, n; a:=[1]: for k from 1 to 65 do
for n from 1 to q do if not isprime(n) and
numboccur(a, n)=0 and isprime(n+a[nops(a)])
then a:=[op(a), n]; break; fi; od; od; a:=subsop(1=NULL, a);
end: P(10^3); # Paolo P. Lava, Jun 05 2019

Mathematica

a = {4}; Do[k = 2 - Boole@ EvenQ@ n; While[Nand[! MemberQ[a, k], CompositeQ@ k, PrimeQ[a[[n - 1]] + k]], k += 2]; AppendTo[a, k], {n, 2, 69}]; a (* Michael De Vlieger, Jul 18 2017 *)

Crossrefs

Cf. A025044, A072525, A085084, A240024.

Sequence in context: A357313 A085084 A248390 * A308289 A236630 A351381

Adjacent sequences: A075567 A075568 A075569 * A075571 A075572 A075573

Keyword

nonn

Author

Amarnath Murthy, Sep 25 2002

Extensions

More terms from David Wasserman, Jan 20 2005

Definition clarified by Peter Munn, Jul 20 2017

Status

approved