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A280997 Primes that have exactly 3 ones in both their binary and ternary expansions. 1

%I

%S 13,37,41,67,97,131,193,577,1033,1153,2053,4129,8209,18433,32771,

%T 32801,32833,65539,133121,525313,557057,1049089,4194433,167772161,

%U 268435459

%N Primes that have exactly 3 ones in both their binary and ternary expansions.

%C Sequence is likely to be finite. If it exists, a(26) > 10^200. - _Robert Israel_, Jan 12 2017

%e 37 is in the sequence because it is a prime and its binary expansion 100101 and ternary expansion 1101 both have exactly 3 ones.

%e 131 is in the sequence because it is a prime and its binary expansion 10000011 and ternary expansion 11212 both have exactly 3 ones.

%p A:= NULL:

%p for a from 2 to 100 do

%p for b from 1 to a-1 do

%p p:= 2^a + 2^b + 1;

%p if numboccur(1, convert(p,base,3)) = 3 and isprime(p) then

%p A:= A, p

%p fi

%p od od:

%p A; # _Robert Israel_, Jan 12 2017

%t Select[Prime[Range[500000]], Count[IntegerDigits[#, 3], 1] == Count[IntegerDigits[#, 2], 1] == 3 &]

%Y Cf. A000040, A001363, A007088, A014311, A066196.

%Y Subset of A281004.

%K nonn,base

%O 1,1

%A _K. D. Bajpai_, Jan 12 2017

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Last modified June 13 20:01 EDT 2021. Contains 345009 sequences. (Running on oeis4.)