A387963 Fixed points of A387819.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 113, 131, 137, 173, 179, 197, 311, 313, 317, 319, 373, 379, 419, 431, 437, 473, 479, 611, 613, 617, 619, 671, 673, 713, 719, 731, 737, 797, 971, 979, 1313, 1319, 1373

Offset

1,2

Comments

The substring may not start with digit 0.

Also, a generalization of the condition in A131648 to every multi-digit substring is prime with respect to 2, 3, 5, 7.

Sequence is finite with a(104) = 67379 the final term.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..104

Formula

{n | A387819(n) = n}.

Example

113 is a term because all its substrings of length greater than 1 are prime numbers.

Prog

(Python)
def children2357(s):
    return set(int(s[:i]+str(q//d)+s[j:]) for i in range(len(s)-1) for j in range(i+2, len(s)+1) if (w:=s[i:j])[0]!='0' for d in [2, 3, 5, 7] if (q:=int(w))%d==0)
def ok(n): return n > 10 and len(children2357(str(n))) == 0
print([k for k in range(1, 10**5) if ok(k)])

Crossrefs

Cf. A131648, A387819.

Sequence in context: A072227 A122427 A161597 * A320320 A263364 A296242

Adjacent sequences: A387960 A387961 A387962 * A387964 A387965 A387966

Keyword

nonn,base,fini,full

Author

Michael S. Branicky and Ali Sada, Oct 12 2025

Status

approved