A271621 a(1) = 2, a(2) = 3, a(n) = A020639(a(n-2)) + A006530(a(n-1)).

2, 3, 5, 8, 7, 9, 10, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset: 1

Author

Cody M. Haderlie, Apr 10 2016

Keywords

• nonn

Comments

Any sequence generated by this formula and any values for a(1) and a(2) will have a finite number of terms not equal to 4; i.e., all such sequences will eventually end up at 4 (and all following terms will be 4; 4 is the only term that can appear more than twice in a row in a sequence because it is the only number equal to the sum of its least and greatest prime factors). Example: a(1) = 77713; a(2) = 16; the sequence is: 77713, 16, 77715, 159, 56, 10, 7, 9, 10, 8, 4, 4, 4, ...

Examples

			a(1) = 13; a(2) = 46.
lpf(13) = 13; gpf(46) = 23.
a(3) = 13 + 23 = 36.
		

Crossrefs

Cf. A020639, A006530, A074320.

Programs

Mathematica

a[1] = 2; a[2] = 3; a[n_] := a[n] = FactorInteger[a[n - 2]][[1, 1]] +
FactorInteger[a[n - 1]][[-1, 1]]; Array[a, {120}] (* Michael De Vlieger, Apr 12 2016 *)

PARI

spf(n) = if (n==1, 1, vecmin(factor(n)[,1]));
gpf(n) = if (n==1, 1, vecmax(factor(n)[,1]));
lista(nn) = {print1(x=2, ", "); print1(y=3, ", "); for (n=1, nn, ny = spf(x) + gpf(y); print1(ny, ", "); x = y; y = ny;);} \\ Michel Marcus, Apr 15 2016

Formula

a(n) = lpf(a(n-2)) + gpf(a(n-1)), where lpf(n) is the least prime dividing n and gpf(n) is the greatest prime dividing n.