A124673 -id:A124673 - cp's OEIS frontend

A124674 Primes with distinct prime digits.

2, 3, 5, 7, 23, 37, 53, 73, 257, 523, 2357, 2753, 3257, 3527, 5237, 5273, 7253, 7523

Offset: 1

Tanya Khovanova, Dec 24 2006

Caldwell and Honaker, 2357, Prime Curios!

Cf. A019546 (primes whose digits are primes), A124673.

Select[Range[10000], PrimeQ[ # ] && Length[IntegerDigits[ # ]] == Length[Union[IntegerDigits[ # ]]] && Complement[IntegerDigits[ # ], {2, 3, 5, 7}] == {} &]

is(k) = isprime(k) && setintersect([2, 3, 5, 7], v=vecsort(digits(k))) == v; \\ Jinyuan Wang, Mar 27 2020

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

Original entry on oeis.org

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

Glen Gilchrist, Jan 20 2023

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.

			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).

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

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

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)))

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A124674 Primes with distinct prime digits.

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

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