Contribution for OEIS

[hv at crypt.org]

Gerald McGarvey <Gerald.McGarvey at comcast.net> wrote:
:So far, except for the 255 term, your sequence agrees
:with sequence A025043 (a(n) not of form prime + a(k), k < n)
:(it has 253 instead)

That'll be because the two sequences boil down to the same definition.

:At 05:56 PM 10/30/2005, Richard Guy wrote:
:>The sequence of P-positions (previous-
:>player-winning positions) in the following
:>nim-like game, played with a heap of beans,
:>from which a move is to take a prime number
:>of beans.  Alternatively, can define a(0)=0,
:>a(1)=1 and a(n) as the least positive integer,
:>bigger than  a(n-1), for which all
:>         a(n)-a(k),    -1 < k < n
:>are composite.  The following was done by hand,
:>so needs checking:
:>
:>   0,   1,   9,  10,  25,  34,  35,  49,  55,  85,
:>  91, 100, 115, 121, 125, 133, 145, 155, 169, 175,
:>187, 195, 205, 217, 235, 247, 255, 259, 265, 289,
:>295, 301, 309, 310, ...

I get as follows:
0 1 9 10 25 34 35 49 55 85 91 100 115 121 125 133 145 155 169 175 187 195
205 217 235 247 253 259 265 289 295 301 309 310 319 325 335 343 355 361 375
385 391 395 403 415 425 445 451 469 475 481 485 493 505 511 515 527 535 545
553 559 565 583 589 595 615 625 637 645 649 655 667 679 685 697 703 715 721

:>Are there infinitely many even members?

The next even member is greater than 1,000,000 if one exists. I find it
hard to believe that another one can exist.

Hugo van der Sanden