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A217044 Primes that remain prime when a single "2" digit is inserted between any two adjacent decimal digits. 8
17, 23, 29, 41, 53, 83, 89, 101, 113, 131, 137, 149, 251, 359, 401, 419, 443, 461, 647, 719, 797, 821, 863, 941, 1289, 1823, 2111, 2543, 3323, 3413, 4013, 4463, 4751, 5021, 5501, 5807, 6299, 6827, 7229, 7643, 7883, 8039, 8219, 8609, 8837, 9221, 9227, 9461, 9623 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Paolo P. Lava and Bruno Berselli, Table of n, a(n) for n = 1..500 (first 123 terms from Paolo Lava)

EXAMPLE

9461 is prime and also 94621, 94261, 92461.

MAPLE

with(numtheory);

A217044:=proc(q, x)

local a, b, c, i, n, ok;

for n from 5 to q do

a:=ithprime(n); b:=0;

while a>0 do b:=b+1; a:=trunc(a/10); od; a:=ithprime(n); ok:=1;

  for i from 1 to b-1 do

    c:=a+9*10^i*trunc(a/10^i)+10^i*x;

    if not isprime(c) then ok:=0; break; fi; od;

  if ok=1 then print(ithprime(n)); fi;

od; end:

A217044(100000, 2)

MATHEMATICA

Select[Prime[Range[5, 1200]], And@@PrimeQ[FromDigits/@Table[ Insert[ IntegerDigits[ #], 2, i], {i, 2, IntegerLength[#]}]]&] (* Harvey P. Dale, Oct 09 2012 *)

PROG

(MAGMA) [p: p in PrimesInInterval(11, 10000) | forall{m: t in [1..#Intseq(p)-1] | IsPrime(m) where m is (Floor(p/10^t)*10+2)*10^t+p mod 10^t}]; // Bruno Berselli, Sep 26 2012

(PARI) is(n)=my(v=concat([""], digits(n))); for(i=2, #v-1, v[1]=Str(v[1], v[i]); v[i]=2; if(i>2, v[i-1]=""); if(!isprime(eval(concat(v))), return(0))); isprime(n)  \\ Charles R Greathouse IV, Sep 26 2012

CROSSREFS

Cf. A050674, A050711-A050719, A069246, A159236, A215417, A215419-A215421, A217045-A217047, A217062-A217065.

Sequence in context: A068581 A166864 A137670 * A145484 A080830 A165566

Adjacent sequences:  A217041 A217042 A217043 * A217045 A217046 A217047

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Sep 25 2012

STATUS

approved

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Last modified November 17 03:06 EST 2019. Contains 329216 sequences. (Running on oeis4.)