A252094 First member of a pair (A,B) to define the n-th Zeisel number, cf. A051015.

1, 4, 1, 2, 3, 2, 10, 2, 6, 4, 13, 8, 3, 2, 25, 5, 9, 28, 1, 6, 5, 17, 34, 15, 9, 23, 8, 49, 55, 12, 4, 33, 14, 2, 24, 36, 25, 2, 26, 4, 2, 42, 29, 11, 8, 2, 10, 4, 88, 6, 47, 32, 48, 20, 94, 37, 23, 57, 24, 3, 5, 115, 6, 118, 9, 44, 3, 46, 68, 5, 30, 139, 50, 10, 51, 14, 77, 20, 54, 2

Offset: 1

Author

Reinhard Zumkeller, Dec 15 2014

Keywords

• nonn

Comments

Let p(0) = 1 and p(i+1) = A*p(i) + B, if p(i) is prime for i = 1..k, then z = p(1) * ... * p(k) is called a Zeisel number.

Examples

			.  n |   A=a(n)  B=A252095(n) | p(1)  p(2)  p(3) | A051015(n)
. ---+------------------------+------------------------------
.  1 |   1       2            |   3     5     7  |        105
.  2 |   4      -1            |   3    11    43  |       1419
.  3 |   1       6            |   7    13    19  |       1729
.  4 |   2       3            |   5    13    29  |       1885
.  5 |   3       2            |   5    17    53  |       4505
.  6 |   2       5            |   7    19    43  |       5719
.  7 |  10      -7            |   3    23   223  |      15387
.  8 |   2       9            |  11    31    71  |      24211
.  9 |   6      -1            |   5    29   177  |      25085
. 10 |   4       3            |   7    31   141  |      27449
. 11 |  13     -10            |   3    29   367  |      31929
. 12 |   8      -3            |   5    37   295  |      54205 .
		

Links

• OEIS Wiki, Zeisel numbers
• Eric Weisstein's World of Mathematics, Zeisel Number.
• Wikipedia, Zeisel number

Crossrefs

Cf. A051015, A027746, A252095 (B values).

Programs

Haskell

a252094 n = a252094_list !! (n-1)
(a252094_list, a252095_list) = unzip $ f 3 where
   f x = if z then (q, p - q) : f (x + 2) else f (x + 2)  where
         z = 0 `notElem` ds && length ds > 2 &&
             all (== 0) (zipWith mod (tail ds) ds) && all (== q) qs
         q:qs = (zipWith div (tail ds) ds)
         ds = zipWith (-) (tail ps) ps
         ps = 1 : ps'; ps'@(p:_) = a027746_row x