A046429 Numbers requiring 9 steps to reach a prime under the prime factor concatenation procedure.

40, 44, 81, 224, 265, 395, 422, 462, 640, 698, 818, 972, 1010, 1032, 1070, 1089, 1174, 1206, 1280, 1336, 1446, 1518, 1520, 1528, 1581, 1662, 1728, 1814, 1816, 1849, 1852, 1853, 1856, 1892, 1927, 1932, 1960, 2032, 2060, 2061, 2090, 2098, 2202, 2212, 2249

Offset: 1

Author

Patrick De Geest, Jun 15 1998

Keywords

• nonn
• base

Examples

			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
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000
• Patrick De Geest, Home Primes

Crossrefs

Cf. A037271, A046411.

Programs

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)
concatelements(v) = my(s = ""); for(i = 1, #v, s = concat(s, v[i])); eval(s)
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

Extensions

Extended and edited by Charles R Greathouse IV, Apr 28 2010