A228445 - OEIS

A228445

Prime numbers with a binary representation in which each digit is repeated at most twice.

2, 3, 5, 11, 13, 19, 37, 41, 43, 53, 73, 83, 89, 101, 107, 109, 149, 173, 179, 181, 211, 293, 307, 331, 347, 409, 421, 587, 601, 613, 617, 619, 659, 661, 677, 683, 691, 809, 811, 821, 853, 857, 859, 877, 1171, 1193, 1229, 1237, 1321, 1381, 1427, 1429, 1433, 1451, 1453, 1459, 1609, 1613, 1619, 1621, 1627, 1637, 1709, 1741

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..64.

FORMULA

A000040 INTERSECT A063037.

EXAMPLE

13 belongs to the list as its binary representation is 1101, in which the first group of 1 consists of 2 repetitions, the first group of 0 consists of only one item and the second group of 1 consists still of only one item; 73 belongs to the list as its binary representation is 1001001, in which 1 is never repeated and 0 is repeated two times.

MAPLE

isA228445 := proc(n)

isprime(n) and isA063037(n) ;

end proc:

for n from 1 to 2000 do

if isA228445(n) then

printf("%d, ", n) ;

end if;

end do: # R. J. Mathar, Dec 18 2013

MATHEMATICA

Select[Prime[Range[300]], Max[Length/@Split[IntegerDigits[#, 2]]]<3&] (* Harvey P. Dale, May 24 2015 *)

CROSSREFS