A380811 Smallest composite number divisible by prime(n) which shares at least one decimal digit with prime(n).

12, 30, 15, 70, 110, 39, 51, 95, 92, 203, 93, 74, 123, 301, 94, 159, 295, 122, 268, 142, 365, 237, 332, 178, 194, 202, 206, 214, 218, 339, 254, 393, 274, 417, 298, 453, 314, 326, 501, 346, 537, 1086, 955, 386, 394, 398, 422, 892, 1362, 916, 932, 956, 482, 502, 514

Offset: 1

Author

David James Sycamore, Feb 04 2025

Keywords

• nonn
• base

Comments

10*prime(n) contains all the digits of prime(n), but is not always the smallest such number.

Examples

			123 is the smallest number divisible by prime(13) = 41 which shares at least one decimal digit (1) of 41, so a(13) = 123.
218 is the smallest number divisible by prime(29) = 109 which shares at least one decimal digit (1) with 109, so a(29) = 218.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Michael De Vlieger, Log log scatterplot of a(n), n = 1..10^6.

Crossrefs

Cf. A000040.

Programs

Mathematica

Table[p = Prime[n]; d = IntegerDigits[p]; m = 1; Until[k = m*p; IntersectingQ[d, IntegerDigits[k]], m++]; k, {n, 120}] (* Michael De Vlieger, Feb 05 2025 *)

PARI

a(n) = my(p = prime(n), d = Set(digits(p))); for(i = 2, oo, if(#setintersect(d, Set(digits(i*p))) > 0, return(i*p))) \\ David A. Corneth, Feb 05 2025

Formula

a(n) <= 10*prime(n), with equality when n = 2,4,5.... (doubtful if there are any more)

Extensions

More terms from David A. Corneth, Feb 05 2025