A134736 a(1) = 5; for n >1, a(n) = a(n-1) + gcd(n, a(n-1)).

5, 6, 9, 10, 15, 18, 19, 20, 21, 22, 33, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 69, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 141, 144, 145, 150, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168

Offset: 1

Author

N. J. A. Sloane, Jan 28 2008

Keywords

• nonn

References

• Eric S. Rowland, A simple prime-generating recurrence, Abstracts Amer. Math. Soc., 29 (No. 1, 2008), p. 50 (Abstract 1035-11-986).

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• Eric S. Rowland, A natural prime-generating recurrence, arXiv:0710.3217 [math.NT], 2007-2008.

Crossrefs

See A106108 for other cross-references.

Cf. A230504, A134743 (first differences), A084662, A084663.

Programs

Haskell

a134736 n = a134736_list !! (n-1)
a134736_list =
   5 : zipWith (+) a134736_list (zipWith gcd a134736_list [2..])
-- Reinhard Zumkeller, Nov 15 2013

Mathematica

a[1] = 5; a[n_] := a[n] = a[n-1] + GCD[n, a[n-1]];
Array[a, 66] (* Jean-François Alcover, Oct 01 2018 *)
RecurrenceTable[{a[1]==5,a[n]==a[n-1]+GCD[n,a[n-1]]},a,{n,70}] (* Harvey P. Dale, Nov 24 2018 *)