|
%I
%S 101,103,107,109,307,401,503,509,601,607,701,709,809,907,10007,10009,
%T 10103,10301,10501,10607,10709,10903,10909,20101,20507,20707,20903,
%U 30103,30307,30509,30703,30803,30809,40009,40507,40709,50707,50909,60103,60107,60509
%N Prime numbers obtained by inserting a 0 between each pair of adjacent digits of a prime number > 10.
%C From _Rémy Sigrist_, Oct 08 2017: (Start)
%C See A159236 for the original prime numbers.
%C The least prime numbers > 10 remaining prime during exactly k iterations of the operation of inserting a 0 between each pair of adjacent digits are, for small values of k:
%C k prime
%C - -----
%C 0 23
%C 1 11
%C 2 19
%C 3 17
%C 4 220333
%C 5 8677267
%C (End)
%e The first four terms arise from 11 -> 101, 13 -> 103, 17 -> 107, 19 -> 109.
%e 23 -> 203 is not prime, so 203 is not a term.
%t a = Table[Table[Mod[Floor[Prime[m]/10^n], 10], {n, 4, 0, -1}], {m, 5, 200}]; Dimensions[a] b = Table[Sum[(If[Mod[n - 1, 2] == 0, a[[m, 1 + Floor[(n - 1)/2]]], 0])*10^(9 - n), {n, 1, 9}], {m, 1, 195}]; c = Flatten[Table[If[PrimeQ[b[[m]]], b[[m]], {}], {m, 1, 195}]]
%o (PARI) forprime (p=10, 599, if (isprime(pp=fromdigits(digits(p), 100)), print1 (pp ", "))) \\ _Rémy Sigrist_, Oct 08 2017
%o (Python)
%o from itertools import count, islice
%o from sympy import isprime, nextprime
%o def ok(n):
%o return n > 10 and isprime(n) and isprime(int("0".join(list(str(n)))))
%o def agen():
%o p = 11
%o while True:
%o t = int("0".join(list(str(p))))
%o if isprime(t): yield t
%o p = nextprime(p)
%o print(list(islice(agen(), 50))) # _Michael S. Branicky_, Jul 11 2022
%Y Cf. A159236.
%K nonn,base
%O 1,1
%A _Roger L. Bagula_, Jun 11 2006
%E Name edited by _Rémy Sigrist_, Oct 08 2017
%E a(39)-a(41) from _Michael S. Branicky_, Jul 11 2022
|
