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A119680 Prime numbers obtained by inserting a 0 between each pair of adjacent digits of a prime number > 10. 1

%I #20 Jul 11 2022 19:55:02

%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

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Last modified March 2 08:59 EST 2024. Contains 370461 sequences. (Running on oeis4.)