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A228445 Prime numbers with a binary representation in which each digit is repeated at most twice. 0
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

Sequence in context: A050229 A224321 A053184 * A287164 A020607 A235631

Adjacent sequences:  A228442 A228443 A228444 * A228446 A228447 A228448

KEYWORD

nonn,base

AUTHOR

Pierandrea Formusa, Nov 06 2013

STATUS

approved

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Last modified December 12 09:36 EST 2019. Contains 329953 sequences. (Running on oeis4.)