A198298 Pandigital numbers (A050278) with each product of adjacent digits visible as a substring of the digits.

3205486917, 3207154869, 4063297185, 4063792185, 4230567819, 4230915678, 4297630518, 4297631805, 5042976318, 5063297184, 5079246318, 5093271486, 5094236718, 5148609327, 5180429763, 5180792463, 5180942367, 5184063297, 5420796318

Offset: 1

Author

Eric Angelini and Jason Kimberley, Jan 03 2012

Keywords

• nonn
• base
• easy
• fini
• full

Comments

There are 58 terms.

Examples

			5x4 ("20") is a substring of 5420976318, as are 4x2 ("8"), 2x0 ("0"), 0x9 ("0"), 9x7 ("63"), 7x6 ("42"), 6x3 ("18"), 3x1 ("3") and 1x8 ("8").
4297631805 is also a member (4*2="8"; 2*9="18"; 9*7="63"; 7*6="42"; 6*3="18"; 3*1="3"; 1*8="8"; 8*0="0"; 0*5="0").
		

Links

• Jason Kimberley, Table of n, a(n) for n = 1..58 (complete sequence)
• Eric Angelini, 10 different digits, 9 products
• Eric Angelini, 10 different digits, 9 products [Cached copy, with permission]
• Eric Angelini, 10 different digits, 9 products, Posting to Seqfan List, Jan 03 2012

Crossrefs

Cf. A203569, A203566, A210013-A210020.

Programs

Python

from itertools import combinations, permutations
def agen():
    c = 0
    digits = list("0123456789")
    for f in digits[1:]:
        rest = digits[:]
        rest.remove(f)
        for p in permutations(rest):
            t = (f, ) + p
            s = "".join(t)
            if all(str(int(t[i])*int(t[i+1])) in s for i in range(9)):
                yield int(s)
afull = list(agen())
print(afull) # Michael S. Branicky, Oct 03 2024