A215420 Primes that remain prime when a single digit 7 is inserted between any two consecutive digits or as the leading or trailing digit.

3, 19, 97, 433, 487, 541, 691, 757, 853, 1471, 2617, 2953, 4507, 6481, 7351, 7417, 8317, 13177, 31957, 42457, 46477, 47977, 50077, 59053, 71917, 73897, 74377, 77479, 77743, 77761, 79039, 99103, 175687, 220897, 271177, 360973

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..63 (all terms up to and including the 1 millionth prime)

Example

59053 is prime as are 590537, 590573, 590753, 597053, 579053, and 759053.

Maple

A215420:=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:
A215420(1000, 7);

Mathematica

Select[Prime[Range[31000]], AllTrue[FromDigits/@Table[Insert[ IntegerDigits[ #], 7, n], {n, IntegerLength[#]+1}], PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 29 2020 *)

Crossrefs

Cf. A215417, A215418, A215419, A215421.

Sequence in context: A049153 A074361 A126187 * A303542 A294251 A294392

Adjacent sequences: A215417 A215418 A215419 * A215421 A215422 A215423

Keyword

nonn,base

Author

Paolo P. Lava, Aug 10 2012

Status

approved