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A217047 Primes that remain prime when a single "8" digit is inserted between any two adjacent digits. 8
11, 23, 47, 83, 131, 173, 179, 233, 353, 389, 521, 569, 641, 683, 839, 887, 911, 971, 983, 1229, 1289, 1913, 2087, 2663, 2837, 2879, 3329, 3671, 3677, 3803, 3821, 4259, 4409, 4817, 4871, 4889, 5237, 5477, 5693, 6449, 6581, 6863, 7283, 7487, 7583, 7823, 7853 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..200

EXAMPLE

325421 is prime and also 3254281, 3254821, 3258421, 3285421 and 3825421.

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, 8)

PROG

(PARI) is(n)=my(v=concat([""], digits(n))); for(i=2, #v-1, v[1]=Str(v[1], v[i]); v[i]=8; if(i>2, v[i-1]=""); if(!isprime(eval(concat(v))), return(0))); isprime(n) \\ Charles R Greathouse IV, Sep 25 2012

(MAGMA) [p: p in PrimesInInterval(11, 8000) | forall{m: t in [1..#Intseq(p)-1] | IsPrime(m) where m is (Floor(p/10^t)*10+8)*10^t+p mod 10^t}]; // Bruno Berselli, Sep 26 2012

CROSSREFS

Cf. A050674, A050711-A050719, A069246, A159236, A215417, A215419-A215421, A217044-A217046.

Sequence in context: A161897 A282531 A145994 * A139834 A100558 A126199

Adjacent sequences:  A217044 A217045 A217046 * A217048 A217049 A217050

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Sep 25 2012

STATUS

approved

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Last modified April 29 01:04 EDT 2017. Contains 285604 sequences.