A360040 Prime numbers missing from A359136: prime numbers for which none of the nontrivial permutations of its digits (permitting leading zeros) produces a prime number.

2, 3, 5, 7, 19, 23, 29, 41, 43, 47, 53, 59, 61, 67, 83, 89, 257, 263, 269, 409, 431, 487, 523, 541, 827, 829, 853, 859, 2861, 4027, 4801, 5209, 5623, 5849

Offset

1,1

Comments

Any prime number p >= 10^11 has necessarily a duplicate digit, say that appears at positions i and j. Applying the nontrivial permutation (i j) to the digits of p yields a prime number (p itself), hence p does not belong to the sequence and the sequence is finite.

All terms belong to A360041.

Links

Table of n, a(n) for n=1..34.

Formula

The nontrivial permutations of the digits of 409 (permitting leading zeros) are:

049 = 7^2,

094 = 2 * 47,

490 = 2 * 5 * 7^2,

904 = 2^3 * 113,

940 = 2^2 * 5 * 47,

so 409 belongs to the sequence.

Prog

(PARI) is(p) = { my (d=digits(p)); if (#d > #Set(d), return (0), forperm (vecsort(d), t, my (q=fromdigits(Vec(t))); if (p!=q && isprime(q), return (0))); return (1)) }

Crossrefs

Cf. A359136, A359137, A360041.

Sequence in context: A391411 A153590 A360041 * A244529 A332583 A345335

Adjacent sequences: A360037 A360038 A360039 * A360041 A360042 A360043

Keyword

nonn,base,fini,full

Author

Rémy Sigrist, Jan 23 2023

Status

approved