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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 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 &]

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

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Last modified November 13 23:01 EST 2019. Contains 329106 sequences. (Running on oeis4.)