A276662 - OEIS

A276662

Iterative procedure in A316941 applied to the odd composite numbers (A071904) (a(n) = -1 if no prime is ever reached).

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

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OFFSET

1,1

COMMENTS

a(n) = A316941(A071904).

LINKS

Table of n, a(n) for n=1..42.

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))