A366897 Brilliant 10-pandigital number (semiprimes whose prime factors are 6-digit numbers) whose prime factors are together 10-pandigital.

12069348751, 13128045769, 13264505987, 13502649817, 14775892063, 14930588627, 15477269803, 15762904837, 15864092773, 15910748263, 16410983527, 16470295813, 16705794823, 16840539127, 17238410569, 18054219637, 18092345567, 18354029467, 18690254753, 19403651287, 19427856073, 19528306417

Offset

1,1

Comments

This sequence contains 66418 terms. - David A. Corneth, Dec 04 2023

Links

Robert Israel, Table of n, a(n) for n = 1..66418

Sean A. Irvine, Java program (github)

Carlos Rivera, Puzzle 1152. 7107379973, The Prime Puzzles and Problems Connection.

Example

a(1) = 12069348751 = 106957 * 112843, because 12069348751 is 10-pandigital (each decimal digit occurs at least one time) and 106957, 112843 are two 6-digit primes and together 10-pandigital.
Table with factors:
  n a(n)
  1 12069348751 = 106957 * 112843
  2 13128045769 = 103549 * 126781
  3 13264505987 = 104789 * 126583
  4 13502649817 = 105619 * 127843
  5 14775892063 = 108929 * 135647
  6 14930588627 = 102769 * 145283
  7 15477269803 = 105727 * 146389
  8 15762904837 = 108203 * 145679
  9 15864092773 = 108929 * 145637

Maple

# this produces the full sequence, but only prints the first 100 terms
P:= select(isprime, [seq(i, i=100001 .. 999999, 2)]): nP:= nops(P):
S:= [seq(convert(convert(P[i], base, 10), set), i=1..nP)]:
Res:= NULL: count:= 0:
for i from 1 to nP do
  for j from i+1 to nP do
    if S[i] union S[j] = {$0..9} and
       convert(convert(P[i]*P[j], base, 10), set) = {$0..9} then
         Res:= Res, P[i]*P[j]: count:= count+1;
     fi
od od:
Res:= sort([Res]):
Res[1..100]; # Robert Israel, Mar 04 2024

Crossrefs

Cf. A001358, A078972, A171102.

Sequence in context: A172587 A172581 A213534 * A202361 A015430 A135496

Adjacent sequences: A366894 A366895 A366896 * A366898 A366899 A366900

Keyword

nonn,base,fini,full

Author

Jean-Marc Rebert, Dec 04 2023

Status

approved