|
Search: id:A114041
|
|
|
| A114041 |
|
Decimal expansion of -x, the real root of the power series with semiprime coefficients. |
|
+0
1
|
|
| 3, 6, 9, 8, 6, 8, 7, 4, 3, 4, 8, 4, 8, 4, 7, 9, 4, 4, 8, 9, 5, 8, 4, 8, 7, 7, 0, 2, 9, 5, 9, 4, 8, 1, 8, 7, 4, 3, 2, 7, 8, 7, 2, 0, 9, 7, 9, 6, 5, 6, 8, 5, 8, 7, 3, 7, 5, 5, 8, 7, 2, 2, 6, 6, 0, 4, 5, 3, 4, 5, 8, 6, 0, 3, 2, 0, 9, 6, 4, 8, 4, 8, 5, 2, 1, 2, 8, 4, 5, 3, 3, 9, 5, 2, 3, 7, 1, 8, 2
(list; cons; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
This is the semiprime analog of A088751 "decimal expansion of -x, the real root of the equation 0 = 1 + Sum{k=1,infinity} prime(k) x^k. The inverse of Backhouse's constant (A072508)." Consider also the polynomial sequence of truncations of this semiprime series, i.e. P_20 = 57*x^20 + 55*x^19 + 51*x^18 + 49*x^17 + 46*x^16 + 39*x^15 + 38*x^14 + 35*x^13 + 34*x^12 + 33*x^11 + 26*x^10 + 25*x^9 + 22*x^8 + 21*x^7 + 15*x^6 + 14*x^5 + 10*x^4 + 9*x^3 + 6*x^2 + 4*x + 1. Interestingly P_3 = 9*x^3 + 6*x^2 + 4*x + 1 = (3*x + 1)(3*x^2 + x + 1), and P_4 = 10*x^4 + 9*x^3 + 6*x^2 + 4*x + 1 = (2*x + 1)(5*x^3 + 2*x^2 + 2*x + 1). Yet P_5 through P_20 are irreducible over Z.
|
|
FORMULA
|
a(n) = digits of -x where x is the real root of 1 + 4x + 6x^2 + 9x^3 + 10x^4 + 14x^5 ... = SUM[from i = 1 to infinity]A001358(i)*x^i.
|
|
EXAMPLE
|
-0.36986874348484794489584877...
|
|
MATHEMATICA
|
Mathematica computation by T. D. Noe (noe(AT)sspectra.com).
|
|
CROSSREFS
|
Cf. A001358, A088751.
Sequence in context: A049341 A137991 A021077 this_sequence A057083 A000748 A011383
Adjacent sequences: A114038 A114039 A114040 this_sequence A114042 A114043 A114044
|
|
KEYWORD
|
cons,nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost2(AT)yahoo.com), Feb 01 2006
|
|
|
Search completed in 0.002 seconds
|
