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A276662
Iterative procedure in A316941 applied to the odd composite numbers (A071904) (a(n) = -1 if no prime is ever reached).
1
311, 1129, 37, 773, 313, 311, 1129, 313, 3119014487, 31079, 317, 773, 1129, 3110647, 3103819425079, 310397, 5113, 31079, 3109, 3137, 310361, 31259, 331, 36389, 191176757654383, 31063, 337, 523, 324941, 31393, 127139, 33769, 31034567124791, 32369, 719, 5623, 347, 3371, 131777, 349, 31039, 34412909
OFFSET
1,1
COMMENTS
a(n) = A316941(A071904).
EXAMPLE
The first entry is from 9 = 3*3. 33 = 3*11, and 311 is prime.
A longer 10 step progression is a(9) from 45. Specifically, 45=3*15 concatenating to 315=3*105 concatenating to 3105=3*1035 concatenating to 31035=3*10345 concatenating to 310345=5*62069 concatenating to 562069=41*13709 concatenating to 4113709=19*216511 concatenating to 19216511=17*1130383 concatenating to 171130383 = 3*57043461 concatenating to 357043461=3*119014487 concatenating to 3119014487 which is prime. a(9) then is 3119014487.
MATHEMATICA
Map[NestWhile[Function[n, FromDigits@ Flatten@ IntegerDigits@ {#, n/#} &[FactorInteger[n][[1, 1]]]], #, ! PrimeQ@ # &] &, Select[Range[9, 157, 2], CompositeQ]] (* Michael De Vlieger, Sep 13 2016 *)
PROG
(PARI) genit(iend)={i5=9; while(i5<=iend, n=i5; while(isprime(n), n+=2); i5=n; endless=0; while(endless<99999, dun=0; z=divisors(n);
a=z[2]; b=n/a; k=length(digits(b)); q=a*10^k+b; if(isprime(q), dun=1; break); endless+=1; n=q); if(dun>0, print1(q, ", ")); i5+=2); }
(Python)
from sympy import primepi, primefactors, factorint
def A276662(n):
if n == 1: return 311
m, k = n, primepi(n) + n + (n>>1)
while m != k:
m, k = k, primepi(k) + n + (k>>1)
while sum((f:=factorint(m)).values()) > 1:
m = int(str(p:=min(f))+str(m//p))
return m # Chai Wah Wu, Aug 02 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Bill McEachen, Sep 11 2016
EXTENSIONS
Edited by N. J. A. Sloane, Oct 02 2016
STATUS
approved