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A217045 Primes that remain prime when a single "4" digit is inserted between any two adjacent decimal digits. 3
19, 37, 43, 61, 67, 73, 97, 109, 199, 211, 223, 241, 349, 409, 421, 457, 463, 541, 571, 751, 757, 823, 991, 1033, 1087, 1321, 1423, 1447, 1543, 2749, 3361, 3469, 3499, 3847, 4111, 4273, 4483, 5059, 5437, 5443, 5449, 6373, 6709, 6793, 7687, 8089, 8221, 8443 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..141

EXAMPLE

87697 is prime and also 876947, 876497, 874697 and 847697.

MAPLE

with(numtheory);

A217045:=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:

A217045(100000, 4)

MATHEMATICA

Select[Prime[Range[5, 1500]], AllTrue[Table[FromDigits[Insert[ IntegerDigits[ #], 4, n]], {n, 2, IntegerLength[#]}], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 04 2017 *)

PROG

(PARI) is(n)=my(v=concat([""], digits(n))); for(i=2, #v-1, v[1]=Str(v[1], v[i]); v[i]=4; 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, A217044, A217046, A217047, A217062-A217065

Sequence in context: A240238 A059695 A134196 * A139313 A272205 A245363

Adjacent sequences:  A217042 A217043 A217044 * A217046 A217047 A217048

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Sep 25 2012

STATUS

approved

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Last modified November 17 05:27 EST 2019. Contains 329217 sequences. (Running on oeis4.)