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%I #30 May 03 2023 15:02:53
%S 0,1,4,6,8,9,10,14,16,18,19,40,46,48,49,60,68,69,80,89,90,104,106,108,
%T 109,146,148,149,168,169,189,406,408,409,468,469,489,608,609,689,809,
%U 1046,1048,1049,1068,1069,1089,1468,1469,1489,1689,4068,4069,4089,4689,6089,10468,10469,10489,10689,14689,40689,104689
%N Numbers whose digits are distinct nonprimes and are not a permutation of a smaller such number.
%C The sequence consists of numbers constructed from the combination of the six nonprime digits 0,1,4,6,8,9 without duplication of the digits. Hence there are 2^6 - 1 = 63 terms.
%e 10 is in the sequence as both 1 and 0 are nonprime, all digits are distinct, and no permutation of those digits yields a smaller number (with no leading 0's).
%e 14 is in the sequence as both 1 and 4 are nonprime, all digits are distinct, and no permutation of those digits yields a smaller number.
%e 41 is not in the sequence as 14 is a permutation of its digits and is a smaller number.
%e 189 is in the sequence, so its permutations 198, 819, 891, 918 and 981, all of which are larger, are not.
%e 104689 is in the sequence as all digits are nonprime and distinct, and no permutation of those digits yields a smaller number (with no leading 0's).
%p sort(map(x-> parse(cat(`if`(nops(x)>1 and x[1]=0,
%p [x[2], x[1], x[3..-1][]], x)[])), [seq(combinat[choose]
%p ([0, 1, 4, 6, 8, 9], i)[], i=1..6)]))[]; # _Alois P. Heinz_, Jan 27 2023
%o (Python)
%o import itertools
%o nums, combinations, flat_list = [0,1,4,6,8,9],[],[]
%o for r in range(len(nums)+1):
%o for combination in itertools.combinations(nums, r):
%o combinations.append(list(combination))
%o for var in range(len(combinations)):
%o subitems=""
%o if (len(combinations[var]) > 1 and combinations[var][0] == 0) :
%o combinations[var][0], combinations[var][1] = combinations[var][1], combinations[var][0]
%o for sub in combinations[var]:
%o subitems += str(sub)
%o flat_list.append(int(subitems))
%o print(sorted(set(flat_list)))
%Y Cf. A062115 (no prime substring), A124673 (distinct prime digits).
%K nonn,base,fini,full
%O 1,3
%A _Glen Gilchrist_, Jan 20 2023
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