Generate equation from pattern

Question

What equation describes the growth pattern of this sequence:

P = 5,25,35,55,65,85,95...

Heres the diferences:

5 (20) 25 (10) 35 (20) 55 (10) 65 ...

I have tried the P = Ax + B but it doesn work since the slope varies from 20 to 10.

Thanks!!

Excluding the first "5" it is "(n+1)th prime × 5". Or you could use Lagrange interpolation $-\frac{2 x^6}{9}+\frac{16 x^5}{3}-\frac{455 x^4}{9}+240x^3-\frac{5348 x^2}{9}+\frac{2189 x}{3}-325$. There are infinite functions that match these points... — kennytm, Apr 14 '15 at 13:29

score 1 · Answer 1 · answered Apr 14 '15 at 13:30

1

I would say :

$$P_n=10(n+E(\frac{n+1}{2}))+5 $$

Where $E(x)$ is the greatest integer which is less or equal to $x$.

answered Apr 14 '15 at 13:30

Clément Guérin

score 1 · Answer 2 · edited Apr 15 '15 at 15:25

1

I found this guys: $$a(n) = \frac52(-3+(-1)^n+6n)$$ Its on OEIS.org. ( OEIS A084957 - multiples of $5$ whose GCD with $6$ is $1$.)

edited Apr 15 '15 at 15:25

achille hui

answered Apr 15 '15 at 14:55

poker3

FYI, I've fixed the formatting plus adding a link to OEIS page. I hope you don't mind. – achille hui Apr 15 '15 at 15:26

2 Answers2