A140948 a(0) = 3; for n >= 1, if a(n-1) = 2*k, then a(n) = k, otherwise 1 + (A065091(n)*a(n-1)), where A065091(n) gives the n-th odd prime.

3, 10, 5, 36, 18, 9, 154, 77, 1772, 886, 443, 16392, 8196, 4098, 2049, 108598, 54299, 3312240, 1656120, 828060, 414030, 207015, 17182246, 8591123, 833338932, 416669466, 208334733, 22291816432, 11145908216, 5572954108, 2786477054, 1393238527, 190873678200, 95436839100, 47718419550, 23859209775

Offset

0,1

Comments

The original name of the sequence: P-adic Hailstone (or A033478): instead of 3, Prime[n] is used: a(n)=If[Mod[a(n - 1), 2] == 0, a(n - 1)/2, Prime(n + 1)*a(n - 1) + 1].

References

C. Pickover, Mazes for the Mind, St. Martin's Press, NY, 1992, p. 203-204.

Links

Antti Karttunen, Table of n, a(n) for n = 0..150

Formula

a(n) = If[Mod[a(n - 1), 2] == 0, a(n - 1)/2, Prime(n + 1)*a(n - 1) + 1].

a(0) = 3; for n >= 1, if a(n-1) = 2*k, then a(n) = k, otherwise 1 + (A065091(n)*a(n-1)). - Antti Karttunen, Jan 29 2016 after the Mathematica-code above and the original name of the sequence.

Mathematica

a[0] = 3; a[n_] := a[n] = If[Mod[a[n - 1], 2] == 0, a[n - 1]/2, Prime[n + 1]*a[n - 1] + 1]; Table[a[n], {n, 0, 30}]

Prog

(Scheme, with memoization-macro definec)
(definec (A140948 n) (cond ((zero? n) 3) ((even? (A140948 (- n 1))) (/ (A140948 (- n 1)) 2)) (else (+ 1 (* (A065091 n) (A140948 (- n 1)))))))
;; Antti Karttunen, Jan 29 2016

Crossrefs

Cf. A033478, A065091.

Sequence in context: A285576 A246777 A111127 * A328763 A281174 A281220

Adjacent sequences: A140945 A140946 A140947 * A140949 A140950 A140951

Keyword

nonn

Author

Roger L. Bagula and Gary W. Adamson, Jul 24 2008

Extensions

Offset corrected, name changed and more terms added by Antti Karttunen, Jan 29 2016

Status

approved