A156770 1 followed by least greater integer such that concatenation of a(n-1) and a(n) is prime.

1, 3, 7, 9, 11, 17, 21, 29, 39, 43, 49, 51, 53, 81, 91, 99, 103, 123, 127, 133, 153, 191, 227, 231, 241, 249, 253, 273, 281, 291, 293, 311, 323, 333, 337, 339, 341, 347, 359, 377, 387, 397, 427, 429, 431, 441, 443, 453, 461, 467, 471, 481, 489, 493, 523, 541

Offset: 1

Author

Gerald Hillier, Feb 15 2009, Mar 13 2010

Keywords

• nonn
• base

Examples

			The term immediately after 17 is 21 because 1721 is the first prime greater than 1717.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..10000

Programs

Maple

cat2 := proc(a,b) a*10^(max(1,ilog10(b)+1))+b ; end: A156770 := proc(n) option remember ; local a; if n = 1 then 1; else for a from procname(n-1)+1 do if isprime( cat2(procname(n-1),a) ) then RETURN(a) ; fi; od: fi; end: seq(A156770(n),n=1..80) ; # R. J. Mathar, Feb 20 2009

Mathematica

nxt[n_]:=Module[{k=n+2,idn=IntegerDigits[n]},While[!PrimeQ[ FromDigits[ Join[ idn, IntegerDigits[ k]]]],k = k+2];k]; NestList[nxt,1,60] (* Harvey P. Dale, Jul 09 2015 *)

Python

from sympy import isprime
from itertools import islice
def agen():
    an = 1
    while True:
        yield an
        s, an = str(an), an+1
        while not isprime(int(s+str(an))): an += 1
print(list(islice(agen(), 56))) # Michael S. Branicky, Oct 17 2022

Extensions

More terms from R. J. Mathar, Feb 20 2009