A345906 Numbers with at least 4 digits such that any 3-digit substring forms a prime number.

1011, 1013, 1017, 1019, 1031, 1037, 1071, 1073, 1079, 1097, 1131, 1137, 1139, 1271, 1277, 1311, 1313, 1317, 1373, 1379, 1397, 1491, 1499, 1571, 1577, 1631, 1673, 1677, 1733, 1739, 1797, 1811, 1911, 1919, 1937, 1971, 1977, 1991, 1997, 2113, 2233, 2239, 2271, 2277, 2293

Offset

1,1

Comments

Only numbers greater than 1000 are considered, since all 3-digit primes are trivial members.

A211684 is a similar sequence that doesn't allow leading zeros in substrings.

Links

Table of n, a(n) for n=1..45.

Example

1011 belongs to the sequence as both 101 and 011=11 are primes.

Maple

q:= n-> (s-> andmap(isprime@parse, [seq(s[j-2..j], j=3..length(s))]))(""||n):
select(q, [$1000..2300])[];  # Alois P. Heinz, Jun 29 2021

Mathematica

Select[Range[1000, 3000], PrimeQ[FromDigits[Take[IntegerDigits[#], -3]]] && PrimeQ[FromDigits[Take[IntegerDigits[#], 3]]] &]

Prog

(Python)
from sympy import isprime
def ok(n):
    if n <= 1000: return False
    s = str(n)
    return all(isprime(int(s[i:i+3])) for i in range(len(s)-2))
print(list(filter(ok, range(1001, 2300)))) # Michael S. Branicky, Jun 29 2021

Crossrefs

Cf. A069489, A211684.

Sequence in context: A235775 A262865 A213315 * A035125 A183849 A185881

Adjacent sequences: A345903 A345904 A345905 * A345907 A345908 A345909

Keyword

nonn,base

Author

Tanya Khovanova, Jun 29 2021

Status

approved