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

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

Cf. A000040, A063037.

Sequence in context: A050229 A224321 A053184 * A287164 A020607 A358719

Adjacent sequences: A228442 A228443 A228444 * A228446 A228447 A228448

Keyword

nonn,base

Author

Pierandrea Formusa, Nov 06 2013

Status

approved