A283209 Primes of the form 299...977...7 with at least one 9 and one 7.

299777, 299977, 29999777, 299999977, 2999999777, 299999999777, 2999977777777, 299999999999977, 2999999999977777777, 2999999999999999977, 299999999999977777777, 299999999999999999977, 2999999999999999777777

Offset: 1

Author

FUNG Cheok Yin, Mar 03 2017

Keywords

• nonn
• base

Comments

If the number of 7's modulo 3 equals 1, the corresponding 29..97..7 term cannot be in sequence because it is divisible by 3.

If the number of 9's modulo 6 equals 5, the corresponding 29..97..7 term cannot be in sequence because 299999 and 999999 are divisible by 7.

If the number of 7's and the number of 9's are both odd, the corresponding 29..97..7 term cannot be in sequence because it is divisible by 11.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..868

Programs

Mathematica

Sort@ Select[Map[FromDigits@ Join[{2}, ConstantArray[9, #1], ConstantArray[7, #2]] & @@ # &, Select[Tuples[Range@ 20, 2], Times @@ Boole@ Map[OddQ, #] == 0 &]], PrimeQ] (* Michael De Vlieger, Mar 06 2017 *)

PARI

do(n)=my(v=List(),p=29,q); for(d=3,n, p=10*p+7; q=p; forstep(i=d-3,1,-1, if(ispseudoprime(q+=2*10^i), listput(v,q)))); Vec(v) \\ Charles R Greathouse IV, Mar 06 2017

Extensions

More terms from Charles R Greathouse IV, Mar 06 2017