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A271621 a(1) = 2, a(2) = 3, a(n) = A020639(a(n-2)) + A006530(a(n-1)). 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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, ...

LINKS

Table of n, a(n) for n=1..75.

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.

EXAMPLE

a(1) = 13; a(2) = 46.

lpf(13) = 13; gpf(46) = 23.

a(3) = 13 + 23 = 36.

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 *)

PROG

(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

CROSSREFS

Cf. A020639, A006530, A074320.

Sequence in context: A182445 A010074 A116918 * A116917 A121369 A284172

Adjacent sequences:  A271618 A271619 A271620 * A271622 A271623 A271624

KEYWORD

nonn

AUTHOR

Cody M. Haderlie, Apr 10 2016

STATUS

approved

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Last modified September 22 12:59 EDT 2021. Contains 347607 sequences. (Running on oeis4.)