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A217065 Primes that remain prime when a single "7" digit is inserted between any two adjacent digits. 7
13, 19, 67, 73, 97, 277, 367, 379, 421, 433, 487, 541, 691, 757, 853, 967, 1117, 1471, 1747, 2017, 2617, 2749, 2851, 2953, 3463, 3529, 3571, 4507, 5077, 5923, 6073, 6079, 6343, 6481, 6577, 6709, 6829, 6967, 7351, 7417, 7573, 7681, 8317, 8719, 9157, 9649, 13177 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..422 (* First 118 terms from Paolo P. Lava *)

EXAMPLE

311683 is prime and also 3116873, 3116783, 3117683, 3171683 and 3711683.

MAPLE

with(numtheory);

A217065:=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:

A217065(1000000, 7);

MATHEMATICA

Select[Prime[Range[5, 1600]], AllTrue[FromDigits/@Table[Insert[ IntegerDigits[ #], 7, i], {i, 2, IntegerLength[#]}], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 12 2016 *)

PROG

(PARI) is(n)=my(v=concat([""], digits(n))); for(i=2, #v-1, v[1]=Str(v[1], v[i]); v[i]=7; 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-A217047, A217062-A217064.

Sequence in context: A180528 A109504 A122042 * A174343 A158332 A241486

Adjacent sequences:  A217062 A217063 A217064 * A217066 A217067 A217068

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Sep 26 2012

STATUS

approved

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Last modified July 24 18:02 EDT 2017. Contains 289776 sequences.