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Pandigital numbers (A050278) with each product of adjacent digits visible as a substring of the digits.
14

%I #40 Oct 04 2024 08:52:48

%S 3205486917,3207154869,4063297185,4063792185,4230567819,4230915678,

%T 4297630518,4297631805,5042976318,5063297184,5079246318,5093271486,

%U 5094236718,5148609327,5180429763,5180792463,5180942367,5184063297,5420796318

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

%C There are 58 terms.

%H Jason Kimberley, <a href="/A198298/b198298.txt">Table of n, a(n) for n = 1..58</a> (complete sequence)

%H Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/DixChiffres.htm">10 different digits, 9 products</a>

%H Eric Angelini, <a href="/A198298/a198298.pdf">10 different digits, 9 products</a> [Cached copy, with permission]

%H Eric Angelini, <a href="http://list.seqfan.eu/oldermail/seqfan/2012-January/016213.html">10 different digits, 9 products</a>, Posting to Seqfan List, Jan 03 2012

%e 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").

%e 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").

%o (Python)

%o from itertools import combinations, permutations

%o def agen():

%o c = 0

%o digits = list("0123456789")

%o for f in digits[1:]:

%o rest = digits[:]

%o rest.remove(f)

%o for p in permutations(rest):

%o t = (f, ) + p

%o s = "".join(t)

%o if all(str(int(t[i])*int(t[i+1])) in s for i in range(9)):

%o yield int(s)

%o afull = list(agen())

%o print(afull) # _Michael S. Branicky_, Oct 03 2024

%Y Cf. A203569, A203566, A210013-A210020.

%K nonn,base,easy,fini,full

%O 1,1

%A Eric Angelini and _Jason Kimberley_, Jan 03 2012