A226972 Emirps whose binary conversion remains emirp when read in decimal.

157, 709, 1283, 1321, 3469, 3929, 9643, 15101, 15241, 15383, 17443, 18439, 19237, 30643, 35911, 38393, 39799, 71711, 73849, 78901, 92381, 92503, 93971, 94219, 98317, 105929, 106427, 106721, 111821, 112481, 123923, 128879, 130693, 146989, 149893, 152407, 165449

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..1691 (numbers < 4*10^7)

Example

For n=1 the a(1)=157 and its reversal 751, both are different and primes. The binary conversion of 157 is 10011101 and its reversal 10111001, both are different and primes.

Maple

with(numtheory):with(StringTools):
  # ====  DECI  EMIRP  ===== BINARY EMIRP ===
  PRS:= proc(x, y)
  local i, a, a1, a2, b, c, d, e, f, g, h, m, count;
  count:=1;
  for i from x to y do;
  a:=ithprime(i);
  a1:=parse(Reverse(convert((a), string)));
  a2:=isprime(a1);
  b:=convert(a, binary);
  c:=isprime(b);
  d:=parse(Reverse(convert((b), string)));
  e:=isprime(d);
  g:=length(a);
  h:= length(d);
  if a2 and c and e and a<>a1 and d<>b then lprint(count, a) ; count:=count+1; fi  ; od;
  lprint("Finished " ):
  end:
  PRS(1, 100000);

Mathematica

Select[Prime@Range@20000, PrimeQ[r = FromDigits@Reverse@IntegerDigits[#]] && r != # && PrimeQ[b = FromDigits[d = IntegerDigits[#, 2]]] && b != (br = FromDigits@ Reverse@d) && PrimeQ[br] &] (* Giovanni Resta, Jun 25 2013 *)

Crossrefs

Cf. A006567 (Emirps, primes whose reversal is a different prime).

Sequence in context: A142833 A142478 A052028 * A337427 A142766 A326442

Adjacent sequences: A226969 A226970 A226971 * A226973 A226974 A226975

Keyword

nonn,base

Author

K. D. Bajpai, Jun 24 2013

Status

approved