cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A069489 Primes > 1000 in which every substring of length 3 is also prime.

This page as a plain text file.
%I A069489 #22 Mar 24 2022 04:00:40
%S A069489 1013,1019,1031,1097,1277,1373,1499,1571,1733,1811,1997,2113,2239,
%T A069489 2293,2719,3079,3137,3313,3373,3491,3499,3593,3673,3677,3733,3739,
%U A069489 3797,4013,4019,4211,4337,4397,4673,4877,4919,5233,5419,5479,6011,6073,6079,6131
%N A069489 Primes > 1000 in which every substring of length 3 is also prime.
%C A069489 Minimum number of digits is taken to be 4 as all 3-digit primes would be trivial members.
%C A069489 Zero may occur only as second digit from left. - _Zak Seidov_, Dec 28 2020
%C A069489 All the digits after the two first digits from left are necessarily odd. - _Bernard Schott_, Mar 20 2022
%H A069489 Reinhard Zumkeller, <a href="/A069489/b069489.txt">Table of n, a(n) for n = 1..1000</a>
%e A069489 11317 is a term as the three substrings of length 3 i.e. 113,131 and 317 all are primes.
%t A069489 Do[ If[ Union[ PrimeQ[ Map[ FromDigits, Partition[ IntegerDigits[ Prime[n]], 3, 1]]]] == {True}, Print[ Prime[n]]], {n, PrimePi[1000] + 1, 10^3}]
%t A069489 Select[Prime[Range[169,800]],AllTrue[FromDigits/@Partition[ IntegerDigits[ #],3,1], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Mar 05 2019 *)
%o A069489 (Haskell)
%o A069489 a069489 n = a069489_list !! (n-1)
%o A069489 a069489_list = filter g $ dropWhile (<= 1000) a000040_list where
%o A069489    g x = x < 100 || a010051 (x `mod` 1000) == 1 && g (x `div` 10)
%o A069489 -- _Reinhard Zumkeller_, Apr 07 2014
%Y A069489 Cf. A069488 and A069490.
%Y A069489 Cf. A211685, A010051, A000040.
%K A069489 nonn,base
%O A069489 1,1
%A A069489 _Amarnath Murthy_, Mar 30 2002
%E A069489 Edited, corrected and extended by _Robert G. Wilson v_, Apr 12 2002