A381248 a(n) = least positive integer m such that m*(m+1) has n-2 distinct digits in base n, all distinct from those (base-n digits) of m and m+1.

1, 4, 14, 156, 20, 750, 1763, 22142, 77776, 64420, 2443077, 52663933, 227623468, 1097568095, 3149642939, 81965144711, 105625962315, 143416754568, 8084207326294, 2574579252942508, 14079288482520493, 68732231173154643, 33344665050312525, 350798169613138819009, 201175550741393337488

Offset: 2

Author

Ali Sada and M. F. Hasler, Feb 17 2025

Keywords

• nonn
• base

Examples

			In base 3, 4*5 = 20 (11*12=202) which has one new digit, 0, that doesn’t exist in 4 or 5.
a(36) is 9725029095719647800676409109. It is XXXXXXXXXXXXXXXXXX in base 36, and XXXXXXXXXXXXXXXXXX * XXXXXXXXXXXXXXXXXY = W048CGKOSX159DHLPT3ZVRNJFB72YUQMIEA6. Every digit is present exactly once in the product. - _Daniel Mondot_, Feb 18 2025
		

Links

• Daniel Mondot, Table of n, a(n) for n = 2..45

Crossrefs

Cf. A381247.

Programs

PARI

apply( {A381248(b=10)=for(n=b^abs(b\/2-1.5)\/1,oo, #setminus(Set(digits(n*(n+1),b)), Set(concat(digits(n,b), digits(n+1,b))))>b-3&&return(n))}, [2..10])

Extensions

a(11)-a(16) from Daniel Mondot, Feb 17 2025

a(17)-a(26) from Michael S. Branicky, Feb 18 2025