A215421 Primes that remain prime when a single digit 9 is inserted between any two consecutive digits or as the leading or trailing digit.

7, 19, 37, 41, 199, 239, 311, 587, 661, 941, 967, 1009, 1997, 4993, 4999, 5393, 5651, 6911, 9109, 9397, 9679, 9829, 19417, 20233, 22549, 27397, 29389, 31387, 39989, 71419, 71569, 90599, 91951, 95369, 97103, 98909, 99023, 160009, 225919, 267389, 313991, 328849

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..100

Example

31387 is prime and also 313879, 313897, 313987, 319387, 391387, 931387.

Maple

A215421:=proc(q, x)
local a, b, c, d, i, n, ok;
for n from 1 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 0 to b 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:
A215421(1000, 9);

Mathematica

Select[Prime[Range[30000]], AllTrue[FromDigits/@Table[Insert[ IntegerDigits[ #], 9, n], {n, IntegerLength[ #]+1}], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 22 2016 *)

Crossrefs

Cf. A215417-A215420

Sequence in context: A298565 A068678 A069833 * A192594 A352243 A031337

Adjacent sequences: A215418 A215419 A215420 * A215422 A215423 A215424

Keyword

nonn,base

Author

Paolo P. Lava, Aug 10 2012

Status

approved