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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: A109504 A122042 A291862 * 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 August 20 00:52 EDT 2018. Contains 313902 sequences. (Running on oeis4.)