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 A084662 a(1) = 4; a(n) = a(n-1) + gcd(a(n-1), n). 24
 4, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES Eric S. Rowland, A simple prime-generating recurrence, Abstracts Amer. Math. Soc., 29 (No. 1, 2008), p. 50 (Abstract 1035-11-986). LINKS Indranil Ghosh, Table of n, a(n) for n = 1..50000 (terms 1..1000 from T. D. Noe) Eric S. Rowland, A simple prime-generating recurrence, arXiv:0710.3217 [math.NT], 2007-2008. MAPLE S := 4; f := proc(n) option remember; global S; if n=1 then S else f(n-1)+igcd(n, f(n-1)); fi; end; MATHEMATICA a[1] = 4; a[n_] := a[n] = a[n - 1] + GCD[n, a[n - 1]]; Table[a[n], {n, 70}] nxt[{n_, a_}] := {n + 1, a + GCD[a, n + 1]}; NestList[nxt, {1, 4}, 70][[All, 2]] (* Harvey P. Dale, Dec 25 2018 *) PROG (Maxima) a[1]:4\$ a[n]:=a[n-1]+gcd(a[n-1], n)\$ makelist(a[n], n, 1, 66); /* Bruno Berselli, May 24 2011 */ (MAGMA) [n eq 1 select 4 else Self(n-1)+Gcd(Self(n-1), n): n in [1..66]]; // Bruno Berselli, May 24 2011 (Haskell) a084662 n = a084662_list !! (n-1) a084662_list =    4 : zipWith (+) a084662_list (zipWith gcd a084662_list [2..]) -- Reinhard Zumkeller, Nov 15 2013 CROSSREFS Cf. A084663, A106108 and other sequences mentioned in A106108. Cf. A230504, A134734 (first differences), A134736. Sequence in context: A010462 A028957 A242664 * A137167 A181564 A119961 Adjacent sequences:  A084659 A084660 A084661 * A084663 A084664 A084665 KEYWORD nonn AUTHOR Matthew Frank (mfrank(AT)wopr.wolfram.com) on behalf of the 2003 New Kind of Science Summer School, Jul 15 2003 STATUS approved

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Last modified August 25 00:02 EDT 2019. Contains 326314 sequences. (Running on oeis4.)