A359982 Numbers whose digits are distinct nonprimes and are not a permutation of a smaller such number.

0, 1, 4, 6, 8, 9, 10, 14, 16, 18, 19, 40, 46, 48, 49, 60, 68, 69, 80, 89, 90, 104, 106, 108, 109, 146, 148, 149, 168, 169, 189, 406, 408, 409, 468, 469, 489, 608, 609, 689, 809, 1046, 1048, 1049, 1068, 1069, 1089, 1468, 1469, 1489, 1689, 4068, 4069, 4089, 4689, 6089, 10468, 10469, 10489, 10689, 14689, 40689, 104689

Offset

1,3

Comments

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.

Links

Table of n, a(n) for n=1..63.

Example

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).
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.
41 is not in the sequence as 14 is a permutation of its digits and is a smaller number.
189 is in the sequence, so its permutations 198, 819, 891, 918 and 981, all of which are larger, are not.
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).

Maple

sort(map(x-> parse(cat(`if`(nops(x)>1 and x[1]=0,
[x[2], x[1], x[3..-1][]], x)[])), [seq(combinat[choose]
([0, 1, 4, 6, 8, 9], i)[], i=1..6)]))[];  # Alois P. Heinz, Jan 27 2023

Prog

(Python)
import itertools
nums, combinations, flat_list = [0, 1, 4, 6, 8, 9], [], []
for r in range(len(nums)+1):
    for combination in itertools.combinations(nums, r):
      combinations.append(list(combination))
for var in range(len(combinations)):
    subitems=""
    if (len(combinations[var]) > 1 and combinations[var][0] == 0) :
      combinations[var][0], combinations[var][1] = combinations[var][1], combinations[var][0]
    for sub in combinations[var]:
        subitems += str(sub)
        flat_list.append(int(subitems))
print(sorted(set(flat_list)))

Crossrefs

Cf. A062115 (no prime substring), A124673 (distinct prime digits).

Sequence in context: A323644 A164702 A001745 * A276628 A050695 A035139

Adjacent sequences: A359979 A359980 A359981 * A359983 A359984 A359985

Keyword

nonn,base,fini,full

Author

Glen Gilchrist, Jan 20 2023

Status

approved