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

1,1

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.

Links

Table of n, a(n) for n=1..59.

Example

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).

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 *)

Prog

(Magma) bs:=func<n|#Divisors(n) eq 3 or &+[d[2]: d in Factorization(n)] eq 2 and #Intseq(Factorization(n)[1][1]) eq #Intseq(Factorization(n)[2][1])>; s:=func<n|&+[d[2]: d in Factorization(n)] eq 2>; 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;

Crossrefs

Cf. A001358, A078972.

Sequence in context: A326063 A085721 A190300 * A081614 A192220 A215477

Adjacent sequences: A338375 A338376 A338377 * A338379 A338380 A338381

Keyword

nonn,base

Author

Marius A. Burtea, Oct 26 2020

Status

approved