A374225 Irregular triangle read by rows: T(n,k), n > 1 and k <= n, is the smallest composite number x whose set of digits and the set of digits in all prime factors of x, when written in base n, contain exactly k digits in common, or -1 if no such number exists.

-1, 9, 4, 4, 8, 6, 15, 4, 6, 14, 30, 114, 4, 12, 10, 35, 190, 894, 4, 8, 33, 188, 377, 2355, 13155, 4, 16, 14, 66, 462, 3269, 22971, 127041, 4, 10, 66, 85, 762, 5359, 36526, 279806, 2219826, 4, 12, 39, 102, 1118, 9096, 62959, 572746, 5053742, 44489860, 4, 12, 95, 132

Offset

2,2

Links

Table of n, a(n) for n=2..57.

Example

T(2, 1) = 9 = 3^2 -> 1001_2 = 11_2^2, have the digit 1 in common, and no lesser composite has this property.
T(6, 2) = 33 = 3 * 11 -> 53_6 = 3_6 * 15_6, have this 2 digits 3 and 5 in common, and no lesser composite has this property.
T(11, 6) = 174752 = 2^5 * 43 * 127 -> 10A326_11 = 2_11^5 * 3A_11 * 106_11, have the 6 digits 0, 1, 2, 3, 6 and A in common, and no lesser composite has this property.
The array begins:
  n\k:0,  1,  2,   3,    4,     5,    6,
  2: -1,  9,  4;
  3:  4,  8,  6,  15;
  4:  4,  6, 14,  30,  114;
  5:  4, 12, 10,  35,  190,   894;
  6:  4,  8, 33, 188,  377,  2355, 13155;

Prog

(PARI)card(base, x)=my(m=factor(x), u=[], v=[], w=[]); my(u=Set(digits(x, base))); for(i=1, #m~, w=Set(digits(m[i, 1], base)); v=setunion(v, w)); #setintersect(u, v)
T(n, k)=my(x); if(k>n, return(0)); if(n==2&&k==0, return(-1)); forcomposite(m=max(2, n^(k-1)), oo, x=card(n, m); if(x==k, return(m)))

Crossrefs

Cf. A358003, A372249, A372280, A372295, A372384, A373645.

Sequence in context: A173571 A275915 A340578 * A199179 A344949 A300072

Adjacent sequences: A374221 A374222 A374223 * A374226 A374227 A374228

Keyword

sign,base,tabl,new

Author

Jean-Marc Rebert, Jul 01 2024

Status

approved