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%I #14 Oct 16 2019 06:17:54
%S 40,44,81,224,265,395,422,462,640,698,818,972,1010,1032,1070,1089,
%T 1174,1206,1280,1336,1446,1518,1520,1528,1581,1662,1728,1814,1816,
%U 1849,1852,1853,1856,1892,1927,1932,1960,2032,2060,2061,2090,2098,2202,2212,2249
%N Numbers requiring 9 steps to reach a prime under the prime factor concatenation procedure.
%H David A. Corneth, <a href="/A046429/b046429.txt">Table of n, a(n) for n = 1..10000</a>
%H Patrick De Geest, <a href="http://www.worldofnumbers.com/topic1.htm">Home Primes</a>
%e 698 is in the sequence as 698 -> 2349 -> 333329 -> 2571297 -> 3857099 -> 31312323 -> 33771937101 -> 379437170413 -> 73124171910091 -> 374148203145623. Only after the ninth iteration we reach a prime. - _David A. Corneth_, Oct 15 2019
%o (PARI) is(n, k) = if(isprime(n), return(0)); for(i = 1, k - 1, n = concatelements(primesvector(n)); if(isprime(n), return(0))); n = concatelements(primesvector(n)); isprime(n)
%o concatelements(v) = my(s = ""); for(i = 1, #v, s = concat(s, v[i])); eval(s)
%o primesvector(n) = my(f = factor(n), res = vector(vecsum(f[,2])), t = 0); for(i = 1, #f~, for(j = 1, f[i, 2], t++; res[t] = f[i, 1])); res \\ _David A. Corneth_, Oct 15 2019
%Y Cf. A037271, A046411.
%K nonn,base
%O 1,1
%A _Patrick De Geest_, Jun 15 1998
%E Extended and edited by _Charles R Greathouse IV_, Apr 28 2010
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