login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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). 0
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 23 00:39 EDT 2021. Contains 348211 sequences. (Running on oeis4.)