A175607 Largest number such that the greatest prime factor of is .

{ 3, 17, 161, 8749, 19601, 246401, 672281, ... } 
It surprised me, but after a little reflection, it makes a lot of sense: for any prime , there is a short (that is to say, finite) list of numbers such that has as its largest prime factor. (See Largest prime dividing .) For example, for , we find that . No larger number satisfies . Evenindexed powers of two are squares of a smaller power of two, and therefore is not an integer if is even. The reason why higher oddindexed powers of two don't work for this purpose is, as so many math textbooks say, left as an exercise for the Reader.
According to Artur Jasinski, every prime has a corresponding with the property described here.
 A239797 Decimal expansion of .
 A238271 Decimal expansion of .
 A237042 UPC check digits.
 A236603 Lowest canonical Gray cycles of length 2n.
 A235365 Smallest odd prime factor of 3^{n} + 1.
 A234522 Decimal expansion of .
 A233748 Number of graphs on n vertices with edges colored with at most four interchangeable colors under the symmetries of the full edge permutation group.
 A232499 Number of unit squares, aligned with a Cartesian grid, completely within the first quadrant of a circle centered at the origin ordered by increasing radius.
 A231963 Concatenate n with its UPC check digit.
 A230624 Numbers n with property that for every base , there is a number m such that m + s(m) = n, where s(m) is the sum of digits in the base b expansion of m.

Sequences in the News
 November 18, 2016 PrimeGrid proves that 10223 is not a Sierpinski number, since 10223 × 2 31172165 + 1 is prime. So no changes to A076336 for now.
 September 14, 2016 Tom Greer discovers the twin primes 2996863034895 × 2 1290000 ± 1 using PrimeGrid, TwinGen and LLR.
 January 19, 2016 Largest known term of A000043 announced: 274207281, also discovered by Curtis Cooper.
 March 2, 2014 Fredrik Johansson announces a computation of the partition number , the largest known term of A000041.
 December 6, 2013 Microsoft launches a challenge to find large nonMersenne primes, A138837.
 May 13, 2013 H. A. Helfgott submits a proof of the weak Goldbach conjecture, i.e. for odd numbers as sums of three primes: A007963 has no more zeroes.
 January 25, 2013 Curtis Cooper discovers a new member of A000043, 57885161. Its index is not known but is at least 48.
 January 13, 2013 The winners of the contest for new sequences in the OEIS at JMM 2013 were announced: A187824, A187771, and A187761.
