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A016837 Primes reached after k iterations of sum of n and its prime divisors = t (where t replaces n in each iteration). 3
23, 11, 23, 17, 11, 23, 23, 23, 17, 47, 19, 41, 23, 23, 47, 53, 41, 59, 29, 31, 47, 71, 47, 47, 41, 71, 71, 89, 71, 167, 83, 47, 53, 47, 71, 113, 59, 71, 71, 269, 83, 131, 59, 167, 71, 167, 59, 149, 167, 71, 167, 191, 83, 71, 167, 79, 89, 179, 251, 227, 167, 149, 149, 83, 269, 239, 89, 167, 251, 263, 251, 251, 113, 239, 149, 167 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Patrick asked what composite would produce 666 or 313 iterations. Carlos has also been working on the problem and asks if there is a run of 3 primes produced by consecutive composites. So original idea belongs to Patrick. This sequence was calculated by Enoch.

LINKS

Robert Israel, Table of n, a(n) for n = 2..10000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 940

FORMULA

Factor n, add n and its prime divisors. Sum = t, t replaces n, repeat until a prime is produced.

EXAMPLE

Starting from 4, 4=2*2, so 4+2+2=8. 8=2*2*2 so 8+2+2+2=14. 14=2*7 so 14+2+7=23, prime is 23 in 3 iterations.

MAPLE

f:= proc(n) option remember; local t;

  t:= n + add(f[1]*f[2], f=ifactors(n)[2]);

  if isprime(t) then return t

  else f(t)

  fi;

end proc:

map(f, [$2 .. 100]); # Robert Israel, Jul 24 2015

PROG

(PARI) sfpn(n) = {my(f = factor(n)); n + sum(k=1, #f~, f[k, 1]*f[k, 2]); }

a(n) = {while (! isprime(t=sfpn(n)), n=t); t; } \\ Michel Marcus, Jul 24 2015

CROSSREFS

Cf. A096461, A018845.

Sequence in context: A128364 A281924 A054574 * A226218 A294087 A323137

Adjacent sequences:  A016834 A016835 A016836 * A016838 A016839 A016840

KEYWORD

easy,nonn

AUTHOR

Enoch Haga, Carlos Rivera, Patrick De Geest

EXTENSIONS

Corrected by Michel Marcus and Robert Israel, Jul 24 2015

STATUS

approved

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Last modified September 23 02:41 EDT 2021. Contains 347609 sequences. (Running on oeis4.)