login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A244862 List of pairs of prime numbers (p,q) starting with (2, 3) such that p || q (where || denotes concatenation) is a prime number and the sequence is always extended with the smallest prime not yet present in the sequence. 2
2, 3, 5, 23, 7, 19, 11, 17, 13, 61, 29, 53, 31, 37, 41, 59, 43, 73, 47, 83, 67, 79, 71, 167, 89, 101, 97, 103, 107, 137, 109, 139, 113, 131, 127, 157, 149, 173, 151, 163, 179, 233, 181, 193, 191, 227, 197, 257, 199, 211, 223, 229, 239, 251, 241, 271, 263, 269, 277, 331, 281, 317, 283, 397, 293, 311, 307, 337, 313, 373, 347, 359, 349, 379, 353 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
The first few pairs are (2,3),(5,23),(7,19),(11,17),(13,61),(29,53), ..., giving the primes 23, 523, 719, 1117, 1361, 2953, ...
MAPLE
with(numtheory):nn:=60:lst:={2, 3}: printf ( "%d %d \n", 2, 3):
for a from 2 to nn do:
p:=ithprime(a):ii:=0:
for b from 1 to nn while(ii=0)do:
q:=ithprime(b):s:=p*10^(length(q))+q:
if type(s, prime)=true and lst intersect {p, q}={}
then
lst:=lst union {p, q}:ii:=1:printf(`%d, `, p):printf(`%d, `, q):
else
fi:
od:
od:
[I have been informed that this program may be incorrect. - N. J. A. Sloane, Jul 03 2024]
# alternative version
P:=proc(q) local a, b, k, i, j, n, ok; a:=[2, 3];
for n from 1 to q do k:=3; ok:=1; for i do if ok=1 then k:=nextprime(k);
if numboccur(k, a)=0 then b:=k;
for j from k do k:=nextprime(k); if numboccur(k, a)=0 then
if isprime(b*10^length(k)+k) then a:=[op(a), b, k]; ok:=0; break; fi; fi; od; fi;
else break; fi; od; od; print(op(a)); end: P(500); # Paolo P. Lava, Jul 03 2024
CROSSREFS
A373794 is a very similar sequence (they first differ at term 69).
Sequence in context: A339228 A013639 A047995 * A373794 A338403 A024782
KEYWORD
nonn,base,tabf
AUTHOR
Michel Lagneau, Jul 25 2014
EXTENSIONS
Edited by N. J. A. Sloane, Jul 03 2024. More than the usual number of terms are shown in order to distinguish this from A373794.
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 24 21:09 EDT 2024. Contains 374585 sequences. (Running on oeis4.)