A368560 a(1) = 78557 (the first Sierpinski number); thereafter a(n+1) = Od(3*5*7*13*19*37*73 - a(n)), where Od(m) is the odd part of m.

78557, 34985939, 2191531, 8482363, 7696009, 31177213, 19436611, 790841, 34629797, 17710319, 13085029, 28482703, 10391933, 29829251, 78557, 34985939, 2191531, 8482363, 7696009, 31177213, 19436611, 790841, 34629797, 17710319, 13085029, 28482703, 10391933, 29829251

Offset: 1

Author

Thomas Ordowski, Dec 30 2023

Keywords

• nonn
• easy

Comments

Generally, if k is a Sierpinski number (or is a Riesel number) and P(k) > k is the product of all elements from the covering set for k*2^n + 1 (or for k*2^n - 1), then Od(P(k) - k) is a Riesel number (or is a Sierpinski number) with the same covering set, where Od(m) is the odd part of m.

Thus a(2n-1) is a Sierpinski number and a(2n) is a Riesel number.

This sequence is purely periodic with period P = 14.

Examples

			a(1) = 78557 is a Sierpinski number and a(2) = (3*5*7*13*19*37*73 - 78557)/2 = 34985939 is a Riesel number with the same covering set {3, 5, 7, 13, 19, 37, 73}.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A000265, A076336, A101036.

Programs

Mathematica

od[n_] := n/2^IntegerExponent[n, 2]; a[1] = 78557; a[n_] := a[n] = od[70050435 - a[n-1]]; Array[a, 42] (* Amiram Eldar, Dec 30 2023 *)

Formula

a(n + 14) = a(n).