A338378 a(1) = 4. a(n) is the smallest semiprime number, which is not an earlier term, for which a(n - 1) + a(n) is a brilliant semiprime number (A078972).

4, 6, 9, 26, 95, 74, 69, 118, 25, 10, 15, 34, 87, 82, 39, 214, 33, 358, 49, 94, 93, 206, 155, 14, 21, 122, 65, 254, 35, 86, 57, 262, 115, 106, 141, 46, 123, 166, 55, 382, 91, 346, 183, 38, 209, 194, 129, 58, 85, 466, 51, 158, 161, 398, 119, 134, 185, 62, 159

Offset: 1

Author

Marius A. Burtea, Oct 26 2020

Keywords

• nonn
• base

Comments

The brilliant semiprime numbers in order of appearance are: 10, 15, 35, 121, 169, 143, 187, 143, 35, 25, 49, 121, 169, 121, 253, 247, 391, 407, 143, 187, 299, 361, 169, 35, 143, 187, 319, 289, 121, 143, ... It is observed that some numbers repeat: 35 = 9 + 26 = 25 + 10 = 14 + 21 or 143 = 74 + 69 = 118 + 25 = 49 + 94 = 21 + 122 = 86 + 57.

Examples

			a(1) + a(2) = 4 + 6 = A001358(1) + A001358(2) = 10 = A078972(4).
a(2) + a(3) = 6 + 9 = A001358(2) + A001358(3) = 15 = A078972(6).
a(3) + a(4) = 9 + 26 = A001358(3) + A001358(10) = 35 = A078972(9).
a(4) + a(5) = 26 + 95 = A001358(10) + A001358(34) = 121 = A078972(11).
		

Crossrefs

Cf. A001358, A078972.

Programs

Magma

bs:=func; s:=func; a:=[ 4 ]; for n in [2..60] do  k:=2; while k in a or  not s(k) or not bs(k+a[n-1]) do k:=k+1; end while; Append(~a,k); end for; a;

Mathematica

Block[{a = {4}}, Do[Block[{k = 6}, While[Nand[FreeQ[a, k], PrimeOmega[k] == 2, If[PrimeOmega[#] == 2, SameQ @@ Map[IntegerLength, FactorInteger[#][[All, 1]] ], False] &[a[[-1]] + k]], k++]; AppendTo[a, k]], {i, 58}]; a] (* Michael De Vlieger, Nov 06 2020 *)