A186000 Consider the list s(1), s(2), ... of numbers that are products of exactly n primes; a(n) is the smallest s(j) whose decimal expansion ends in j.

1, 17, 291, 12, 56, 78645, 1350, 192, 896, 7936, 36096, 3072, 14336, 250880, 1247232, 49152, 229376, 4014080, 6718464, 786432, 3670016, 64225280, 45203456000, 12582912, 58720256, 622854144, 219792015360, 201326592, 939524096, 8321499136, 37849399296, 3221225472, 15032385536, 263066746880, 2924872728576, 51539607552, 240518168576, 4209067950080, 7044820107264, 824633720832, 3848290697216

Offset: 0

Author

Jonathan Vos Post and Robert G. Wilson v, Feb 24 2011

Keywords

• nonn
• base
• changed

Comments

For n = 0, 1, 2, ..., the index j corresponding to a(n) is 1, 7, 91, 2, 6, 8645, 50, 2, 6, 36, 96, 2, 6, 80, 232, 2, 6, 80, 64, 2, 6, 80, >6136, 2, 6, 44, > 564, 2, 6, 36, 96, 2, 6, 80, >286, 2, 6, 80, 64, 2, 6, ..., .

Examples

			a(0) = 1 because 1 is the first and only positive integer (A000027) which is not a prime, a semiprime, a triprime, etc.;
a(1) = 17 because 17 is the seventh term of A000040 (it is also the first term of A046883);
a(2) = 291 because 291 is the 91st term of A001358;
a(3) = 12 because 12 is the second term of A014612;
a(4) = 56 because 56 is the sixth term of A014613; etc.
		

Links

• Index entries for sequences related to automorphic numbers

Crossrefs

Cf. A000040, A001358, A046883, A014612, A014613, A078840, A185999.

Programs

Mathematica

nextKthAlmostPrime[n_, k_] := Block[{m = n + 1}, While[ Plus @@ Last /@ FactorInteger@ m != k, m++]; m] (* Eric W. Weisstein, Feb 07 2006 *); f[n_] := Block[{c = 1, kp = 2^n}, While[ Mod[kp, 10^Floor[1 + Log10@ c]] != c, c++; kp = nextKthAlmostPrime[kp, n]]; kp]
(* These terms can be crosschecked by: *)
AlmostPrimePi[k_Integer, n_] := Module[{a, i}, a[0] = 1; If[k == 1, PrimePi[n], Sum[PrimePi[n/Times @@ Prime[Array[a, k - 1]]] - a[k - 1] + 1, Evaluate[ Sequence @@ Table[{a[i], a[i - 1], PrimePi[(n/Times @@ Prime[Array[a, i - 1]])^(1/(k - i + 1))]}, {i, k - 1}]]]]] (* Eric W. Weisstein, Feb 07 2006 *)

Extensions

Edited by N. J. A. Sloane, Mar 04 2011

The missing values, a(22), a(26) & a(34), were supplied to me via email dtd Mar 03 2011 from Donovan Johnson. - Robert G. Wilson v, Mar 22 2011