

A280997


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


1



13, 37, 41, 67, 97, 131, 193, 577, 1033, 1153, 2053, 4129, 8209, 18433, 32771, 32801, 32833, 65539, 133121, 525313, 557057, 1049089, 4194433, 167772161, 268435459
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Sequence is likely to be finite. If it exists, a(26) > 10^200.  Robert Israel, Jan 12 2017


LINKS

Table of n, a(n) for n=1..25.


EXAMPLE

37 is in the sequence because it is a prime and its binary expansion 100101 and ternary expansion 1101 both have exactly 3 ones.
131 is in the sequence because it is a prime and its binary expansion 10000011 and ternary expansion 11212 both have exactly 3 ones.


MAPLE

A:= NULL:
for a from 2 to 100 do
for b from 1 to a1 do
p:= 2^a + 2^b + 1;
if numboccur(1, convert(p, base, 3)) = 3 and isprime(p) then
A:= A, p
fi
od od:
A; # Robert Israel, Jan 12 2017


MATHEMATICA

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


CROSSREFS

Cf. A000040, A001363, A007088, A014311, A066196.
Subset of A281004.
Sequence in context: A301591 A301857 A220462 * A185006 A285887 A063913
Adjacent sequences: A280994 A280995 A280996 * A280998 A280999 A281000


KEYWORD

nonn,base


AUTHOR

K. D. Bajpai, Jan 12 2017


STATUS

approved



