A329711 Numbers n such that n = prime(d_1) * prime(d_2) * ... * prime(d_k), where n is a concatenation of d_1, d_2, ..., d_k.
14, 154, 1196, 2127, 61411, 172482, 223227, 279174, 291318, 1233822, 1346235, 2681318, 3127010, 6541482, 9105217, 14216826, 15136418, 15454362, 17211896, 22442133, 24174129, 32693925, 35219085, 35523825, 51157348, 51431138, 57121662, 58935162, 91242978, 101721214
Offset: 1
Examples
14 = prime(1)*prime(4) = 2*7, so 14 is a term. 154 = prime(1)*prime(5)*prime(4) = 2*11*7, so 154 is a term. 2127 = prime(2)*prime(127) = 3*709, so 2127 is a term. 9105217 = prime(9)*prime(10)*prime(5)*prime(21)*prime(7), so 9105217 is a term.
Links
- Giovanni Resta, Table of n, a(n) for n = 1..191
- Bartlomiej Pawlik, Table of concatenations and prime factorizations of a(n) for n = 1..191
Programs
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Mathematica
ok[n_] := Block[{d = DigitCount@ n}, AllTrue[Range@ 9, IntegerExponent[n, Prime@ #] <= d[[#]] &]]; ric[v_, d_] := If[PrimeQ@ v, PrimePi@ v == FromDigits@ d, Block[ {r=False, p, m = Length@ d}, Do[ If[ d[[i + 1]] > 0, p = Prime@ FromDigits@ Take[d, i]; If[Mod[v, p] == 0 && (r = ric[v/p, Take[d, i - m]]), Break[]]], {i, m - 1}]; r]]; Select[ Range@ 300000, If[ok@# && ric[#, IntegerDigits@ #], Print@#; True, False] &] (* Giovanni Resta, Mar 12 2020 *)
Extensions
More terms from Giovanni Resta, Mar 12 2020