cp's OEIS Frontend

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

%I A198298 #41 Dec 23 2024 14:53:42
%S A198298 3205486917,3207154869,4063297185,4063792185,4230567819,4230915678,
%T A198298 4297630518,4297631805,5042976318,5063297184,5079246318,5093271486,
%U A198298 5094236718,5148609327,5180429763,5180792463,5180942367,5184063297,5420796318
%N A198298 Pandigital numbers (A050278) with each product of adjacent digits visible as a substring of the digits.
%C A198298 There are 58 terms.
%H A198298 Jason Kimberley, <a href="/A198298/b198298.txt">Table of n, a(n) for n = 1..58</a> (complete sequence)
%H A198298 Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/DixChiffres.htm">10 different digits, 9 products</a>
%H A198298 Eric Angelini, <a href="/A198298/a198298.pdf">10 different digits, 9 products</a> [Cached copy, with permission]
%H A198298 Eric Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2012-January/016213.html">10 different digits, 9 products</a>, Posting to Seqfan List, Jan 03 2012
%e A198298 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 A198298 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 A198298 (Python)
%o A198298 from itertools import combinations, permutations
%o A198298 def agen():
%o A198298     c = 0
%o A198298     digits = list("0123456789")
%o A198298     for f in digits[1:]:
%o A198298         rest = digits[:]
%o A198298         rest.remove(f)
%o A198298         for p in permutations(rest):
%o A198298             t = (f, ) + p
%o A198298             s = "".join(t)
%o A198298             if all(str(int(t[i])*int(t[i+1])) in s for i in range(9)):
%o A198298                 yield int(s)
%o A198298 afull = list(agen())
%o A198298 print(afull) # _Michael S. Branicky_, Oct 03 2024
%Y A198298 Cf. A203569, A203566, A210013-A210020.
%K A198298 nonn,base,easy,fini,full
%O A198298 1,1
%A A198298 Eric Angelini and _Jason Kimberley_, Jan 03 2012