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

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

Offset: 1

Author

K. D. Bajpai, Jan 12 2017

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Crossrefs

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

Subset of A281004.

Programs

Maple

A:= NULL:
for a from 2 to 100 do
  for b from 1 to a-1 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 &]
Select[Prime[Range[300000]],DigitCount[#,2,1]==DigitCount[#,3,1]==3&] (* The program generates the first 23 terms of the sequence. *) (* Harvey P. Dale, Jul 20 2025 *)