A135167 a(n) = 7^n + 5^n + 3^n - 2^n. Constants are the prime numbers in decreasing order.

2, 13, 79, 487, 3091, 20143, 133939, 903727, 6161731, 42325903, 292298899, 2026329967, 14085955171, 98111299663, 684331355059, 4778093404207, 33385561441411, 233393582449423, 1632228682334419, 11417969833438447, 79887637214988451, 559022711699743183, 3912205265750868979

Offset: 0

Author

Omar E. Pol, Nov 21 2007

Keywords

• easy
• nonn

Examples

			a(4)=3091 because 7^4=2401, 5^4=625, 3^4=81, 2^4=16 and we can write 2401+625+81-16=3091.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (17,-101,247,-210).

Crossrefs

Cf. A000079, A000244, A000351, A000420, A001047, A074527, A007689, A135158, A135159, A135160.

Programs

Magma

[7^n+5^n+3^n-2^n: n in [0..50]]; // Vincenzo Librandi, Dec 15 2010

Mathematica

Table[7^n + 5^n + 3^n - 2^n, {n, 0,50}] (* or *) LinearRecurrence[{17, -101, 247, -210}, {2, 13, 79, 487}, 50] (* G. C. Greubel, Sep 30 2016 *)

PARI

a(n)=7^n+5^n+3^n-2^n \\ Charles R Greathouse IV, Sep 30 2016

Formula

a(n) = 7^n + 5^n + 3^n - 2^n.

From G. C. Greubel, Sep 30 2016: (Start)

a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4).

G.f.: (2 - 21*x + 60*x^2 - 37*x^3)/((1 -2*x)*(1 -3*x)*(1 -5*x)*(1 -7*x)).

E.g.f.: exp(7*x) + exp(5*x) + exp(3*x) - exp(2*x). (End)

Extensions

More terms from Vincenzo Librandi, Dec 15 2010