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

1,2

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.

Links

Table of n, a(n) for n=1..80.

OEIS Wiki, Zeisel numbers

Eric Weisstein's World of Mathematics, Zeisel Number.

Wikipedia, Zeisel number

Example

.  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 .

Prog

(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

Crossrefs

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

Sequence in context: A375576 A064124 A106654 * A196138 A198185 A197889

Adjacent sequences: A252091 A252092 A252093 * A252095 A252096 A252097

Keyword

nonn

Author

Reinhard Zumkeller, Dec 15 2014

Status

approved