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A050707 Composites c that reach a prime after 3 iterations of c -> c + sum of prime factors of c. 7
4, 16, 27, 28, 30, 42, 76, 87, 92, 95, 108, 114, 120, 124, 128, 133, 136, 147, 148, 154, 172, 196, 202, 204, 216, 222, 238, 242, 243, 244, 245, 255, 256, 260, 285, 286, 292, 308, 310, 325, 338, 340, 342, 350, 386, 412, 418, 422, 423, 426, 435, 440, 458, 464 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1001 [offset shifted by Georg Fischer, Oct 29 2019]

EXAMPLE

204 is a term:

Iteration 1: 204 = 2*2*3*17 so 204 + (2+2+3+17) = 204 + 24 = 228 and composite.

Iteration 2: 228 = 2*2*3*19 so 228 + (2+2+3+19) = 228 + 26 = 254 and composite.

Iteration 3: 254 = 2*127 so 254 + (2+127) = 254 + 129 = 383 and prime.

MATHEMATICA

nxt[n_]:=Total[Flatten[Table[#[[1]], {#[[2]]}]&/@FactorInteger[n]]]+n; Select[ Range[500], PrimeQ[NestList[nxt, #, 3]]=={False, False, False, True}&] (* Harvey P. Dale, Feb 23 2014 *)

PROG

(MAGMA) f:=func<n|n+(&+[j[1]*j[2]: j in Factorization(n)]) >; a:=[]; for k in [4..500] do if not IsPrime(k) and not IsPrime(f(k)) and not IsPrime(f(f(k))) and IsPrime(f(f(f(k)))) then Append(~a, k); end if; end for; a; // Marius A. Burtea, Oct 17 2019

CROSSREFS

Cf. A050703, A050704, A050705, A050706, A050708, A050709, A050710.

Sequence in context: A223221 A210002 A105078 * A046346 A134330 A340852

Adjacent sequences:  A050704 A050705 A050706 * A050708 A050709 A050710

KEYWORD

nonn

AUTHOR

Patrick De Geest, Aug 15 1999

EXTENSIONS

Name edited by Michel Marcus, Oct 17 2019

STATUS

approved

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Last modified April 10 10:39 EDT 2021. Contains 342845 sequences. (Running on oeis4.)