A085908 Smallest 7-smooth number beginning with n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 112, 12, 135, 14, 15, 16, 175, 18, 192, 20, 21, 224, 2304, 24, 25, 2625, 27, 28, 294, 30, 315, 32, 336, 343, 35, 36, 375, 384, 392, 40, 4116, 42, 432, 441, 45, 4608, 4704, 48, 49, 50, 512, 525, 5376, 54, 55125, 56, 576, 588, 59049, 60

Offset

0,2

Links

Table of n, a(n) for n=0..59.

Example

a(23) = 2304 = 2^8*3^2 is the smallest 7-smooth number beginning with 23. (23, 230, 231, 232, ..., 239, 2301, 2302, 2303 etc. have a divisor > 10.)

Mathematica

a[n_] := Module[{d = IntegerDigits[n], k = 1}, While[Max[FactorInteger[k][[;; , 1]]] > 7 || Length[IntegerDigits[k]] < Length[d] || IntegerDigits[k][[1 ;; Length[d]]] != d, k++]; k]; Array[a, 60] (* Amiram Eldar, Apr 30 2022 *)

Prog

(PARI) hc(n) = local(f); f = factor(n); f[matsize(f)[1], 1] < 10;
a(n) = local(d, x); if (hc(n), return(n)); d = 1; while (d, for (i = 1, 10^d - 1, x = n*10^d + i; if (hc(x), return(x))); d++); \\ David Wasserman, Feb 11 2005

Crossrefs

Cf. A002473.

Sequence in context: A258373 A250266 A357936 * A110304 A043315 A044912

Adjacent sequences: A085905 A085906 A085907 * A085909 A085910 A085911

Keyword

base,nonn

Author

Amarnath Murthy, Jul 09 2003

Extensions

Corrected and extended by David Wasserman, Feb 11 2005

Name corrected by J. Lowell, Apr 30 2022

Status

approved