A211684 Numbers > 1000 such that all the substrings of length = 3 are primes (substrings with leading '0' are considered to be nonprime).

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, 2331, 2337, 2397, 2419, 2571

Offset

1,1

Comments

Only numbers > 1000 are considered, since all 3-digit primes are trivial members. See A069489 for the sequence with prime terms > 1000.

The sequence is infinite (for example, consider the continued concatenation of '19' or of '337': 1919, 19191, 191919, ..., 3373, 33733, 337337, ... are members).

Infinitely many terms are palindromic.

A 10-automatic sequence realized by a linear recurrence relation. - Charles R Greathouse IV, Jan 04 2013

There are 204 4-digit terms. - Harvey P. Dale, Apr 09 2026

Links

Hieronymus Fischer, Table of n, a(n) for n = 1..3000

Index entries for 10-automatic sequences.

Example

a(1) = 1131, since all substrings of length = 3 (113 and 131) are primes.
a(33) = 2271, since all substrings of length = 3 (227, 271) are primes.

Mathematica

Select[Range[1000, 9999], With[{c=IntegerDigits[#]}, c[[2]]!=0&&AllTrue[FromDigits/@{Most[c], Rest[c]}, PrimeQ]]&] (* The program generates all 4-digit terms. *) (* Harvey P. Dale, Apr 09 2026 *)

Crossrefs

Cf. A019546, A035232, A039996, A046034, A069489, A085823, A211681, A211682.

Sequence in context: A023307 A163560 A252287 * A162023 A166957 A163651

Adjacent sequences: A211681 A211682 A211683 * A211685 A211686 A211687

Keyword

nonn,base,easy

Author

Hieronymus Fischer, Jun 08 2012

Status

approved