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

%I A252094 #5 Feb 16 2025 08:33:24
%S A252094 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,
%T A252094 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,
%U A252094 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
%N A252094 First member of a pair (A,B) to define the n-th Zeisel number, cf. A051015.
%C A252094 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.
%H A252094 OEIS Wiki, <a href="https://oeis.org/wiki/Zeisel_numbers">Zeisel numbers</a>
%H A252094 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ZeiselNumber.html">Zeisel Number.</a>
%H A252094 Wikipedia, <a href="http://en.wikipedia.org/wiki/Zeisel_number">Zeisel number</a>
%e A252094 .  n |   A=a(n)  B=A252095(n) | p(1)  p(2)  p(3) | A051015(n)
%e A252094 . ---+------------------------+------------------------------
%e A252094 .  1 |   1       2            |   3     5     7  |        105
%e A252094 .  2 |   4      -1            |   3    11    43  |       1419
%e A252094 .  3 |   1       6            |   7    13    19  |       1729
%e A252094 .  4 |   2       3            |   5    13    29  |       1885
%e A252094 .  5 |   3       2            |   5    17    53  |       4505
%e A252094 .  6 |   2       5            |   7    19    43  |       5719
%e A252094 .  7 |  10      -7            |   3    23   223  |      15387
%e A252094 .  8 |   2       9            |  11    31    71  |      24211
%e A252094 .  9 |   6      -1            |   5    29   177  |      25085
%e A252094 . 10 |   4       3            |   7    31   141  |      27449
%e A252094 . 11 |  13     -10            |   3    29   367  |      31929
%e A252094 . 12 |   8      -3            |   5    37   295  |      54205 .
%o A252094 (Haskell)
%o A252094 a252094 n = a252094_list !! (n-1)
%o A252094 (a252094_list, a252095_list) = unzip $ f 3 where
%o A252094    f x = if z then (q, p - q) : f (x + 2) else f (x + 2)  where
%o A252094          z = 0 `notElem` ds && length ds > 2 &&
%o A252094              all (== 0) (zipWith mod (tail ds) ds) && all (== q) qs
%o A252094          q:qs = (zipWith div (tail ds) ds)
%o A252094          ds = zipWith (-) (tail ps) ps
%o A252094          ps = 1 : ps'; ps'@(p:_) = a027746_row x
%Y A252094  Cf. A051015, A027746, A252095 (B values).
%K A252094 nonn
%O A252094 1,2
%A A252094 _Reinhard Zumkeller_, Dec 15 2014