A236528 Start with 4; thereafter, primes obtained by concatenating to the end of previous term the next smallest number that will produce a prime.

4, 41, 419, 41911, 4191119, 41911193, 419111933, 41911193341, 4191119334151, 419111933415151, 41911193341515187, 4191119334151518719, 419111933415151871963, 41911193341515187196323, 4191119334151518719632313, 419111933415151871963231329

Offset

1,1

Comments

a(n+1) is the next smallest prime beginning with a(n). Initial term is 4.

After a(1), these are the primes arising in A069606.

Links

Table of n, a(n) for n=1..16.

Example

a(1) = 4 by definition.
a(2) is the next smallest prime beginning with 4, so a(2) = 41.
a(3) is the next smallest prime beginning with 41, so a(3) = 419.
...and so on.

Mathematica

NestList[Module[{k=1}, While[!PrimeQ[#*10^IntegerLength[k]+k], k+=2]; #*10^IntegerLength[k]+ k]&, 4, 20] (* Harvey P. Dale, Jul 20 2024 *)

Prog

(Python)
import sympy
from sympy import isprime
def b(x):
..num = str(x)
..n = 1
..while n < 10**3:
....new_num = str(x) + str(n)
....if isprime(int(new_num)):
......print(int(new_num))
......x = new_num
......n = 1
....else:
......n += 1
b(4)

Crossrefs

Cf. A110773, A048553, A069606.

Sequence in context: A193368 A109109 A227996 * A114467 A118450 A024383

Adjacent sequences: A236525 A236526 A236527 * A236529 A236530 A236531

Keyword

nonn,base

Author

Derek Orr, Jan 27 2014

Status

approved