Number Theory

Notice that the odd-numbered terms, 1, 3, 5, 7........etc have a difference of 36, and the even-numbered terms, 2, 4, 6.....etc,  have a difference of 45!!.

So, the next 5 terms  are: 262+36=298, 350+45 =395, 298+36 =334, 395+45=440, 334+36=370.

So, the next 5 term are:298, 395, 334, 440, 370.......etc.

I noticed that this sequence alternates between the sum of first 4 counting numbers and the sum of the next 5 counting numbers: [1+2+3+4=10], [5+6+7+8+9=35], [10+11+12+13=46], [14+15+16+17+18=80]....etc.