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