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A119680 Prime numbers obtained by inserting a 0 between each pair of adjacent digits of a prime number > 10. 1
101, 103, 107, 109, 307, 401, 503, 509, 601, 607, 701, 709, 809, 907, 10007, 10009, 10103, 10301, 10501, 10607, 10709, 10903, 10909, 20101, 20507, 20707, 20903, 30103, 30307, 30509, 30703, 30803, 30809, 40009, 40507, 40709, 50707, 50909, 60103, 60107, 60509 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From Rémy Sigrist, Oct 08 2017: (Start)

See A159236 for the original prime numbers.

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:

k prime

- -----

0 23

1 11

2 19

3 17

4 220333

5 8677267

(End)

LINKS

Table of n, a(n) for n=1..41.

EXAMPLE

The first four terms arise from 11 -> 101, 13 -> 103, 17 -> 107, 19 -> 109.

23 -> 203 is not prime, so 203 is not a term.

MATHEMATICA

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}]]

PROG

(PARI) forprime (p=10, 599, if (isprime(pp=fromdigits(digits(p), 100)), print1 (pp ", "))) \\ Rémy Sigrist, Oct 08 2017

(Python)

from itertools import count, islice

from sympy import isprime, nextprime

def ok(n):

return n > 10 and isprime(n) and isprime(int("0".join(list(str(n)))))

def agen():

p = 11

while True:

t = int("0".join(list(str(p))))

if isprime(t): yield t

p = nextprime(p)

print(list(islice(agen(), 50))) # Michael S. Branicky, Jul 11 2022

CROSSREFS

Cf. A159236.

Sequence in context: A309488 A134809 A256186 * A329737 A166571 A201965

Adjacent sequences: A119677 A119678 A119679 * A119681 A119682 A119683

KEYWORD

nonn,base

AUTHOR

Roger L. Bagula, Jun 11 2006

EXTENSIONS

Name edited by Rémy Sigrist, Oct 08 2017

a(39)-a(41) from Michael S. Branicky, Jul 11 2022

STATUS

approved

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Last modified February 5 02:00 EST 2023. Contains 360082 sequences. (Running on oeis4.)