side to side

[md2]

next values :

I : 2 + 2 ^ 2

II : 2 + 2 ^ 3

III : 2 ^ 1 + 2 ^ 2 + 2 ^ 3

Edited June 16, 2014 by md2

[Acme]

next values :

I : 2 + 2 ^ 2

II : 2 + 2 ^ 3

wrong to wrong No value. Last chance?

[pzkpfw]

The policeman's beard is half constructed.

[imatfaal]

next values :

I : 2 + 2 ^ 2

II : 2 + 2 ^ 3

III : 2 ^ 1 + 2 ^ 2 + 2 ^ 3

2,6,10,14,18,22,26,30,34,38

 

Arithmetic Progression

 

initial term = 2

common difference = 4

 

[Acme]

2,6,10,14,18,22,26,30,34,38

 

Arithmetic Progression

 

initial term = 2

common difference = 4

a_n = 2(2n-1)

or

4n-2

n={1,2,3...}

[imatfaal]

a_n = 2(2n-1)

or

4n-2

n={1,2,3...}

 

I prefer my phrasing. APs have an initial value a_1 and following iterations have a common difference. You want to be able to shoehorn it into this a_n = a_1 +(n-1)d. Your representation are correct - but you would have to hand do any investigation to the progression; whereas many short-cut formulae are available if the phrasing is traditional

[Acme]

I prefer my phrasing. APs have an initial value a_1 and following iterations have a common difference. You want to be able to shoehorn it into this a_n = a_1 +(n-1)d. Your representation are correct - but you would have to hand do any investigation to the progression; whereas many short-cut formulae are available if the phrasing is traditional

It is always my pleasure to append a correct addition to one of your preferred phrasings.

Here is md2's AP plotted on Ulam's spiral. From this we can tell at a glance that the AP contains no Perfect Squares.

 

{2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 98, 102, 106, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, 186, 190, 194, 198, 202, 206, 210, 214, 218, 222, 226, 230, 234, 238, 242, 246, 250, 254, 258, 262, 266, 270, 274, 278, 282, 286, 290, 294, 298, 302, 306, 310, 314, 318, 322, 326, 330, 334, 338, 342, 346, 350, 354, 358, 362, 366, 370, 374, 378, 382, 386, 390, 394, 398, 402, 406, 410, 414, 418, 422, 426, 430, 434, 438, 442, 446, 450, 454, 458, 462, 466, 470, 474, 478, 482, 486, 490, 494, 498, 502, 506, 510, 514, 518, 522, 526, 530, 534, 538, 542, 546, 550, ...}