A175330 a(n) = bitwise AND of prime(n) and prime(n+1).

2, 1, 5, 3, 9, 1, 17, 19, 21, 29, 5, 33, 41, 43, 37, 49, 57, 1, 67, 65, 73, 67, 81, 65, 97, 101, 99, 105, 97, 113, 3, 129, 137, 129, 149, 149, 129, 163, 165, 161, 177, 181, 129, 193, 197, 195, 211, 195, 225, 225, 233, 225, 241, 1, 257, 261, 269, 261, 273, 281

Offset: 1

Author

Leroy Quet, Apr 07 2010

Keywords

• base
• nonn

Comments

Read each binary representation of the primes from right to left and then AND respective digits to form the binary equivalent of each term of this sequence.

Indices of 1's: 2, 6, 18, 54, 564, 3512, 6542, 564163, 2063689, 54400028, ... - Alex Ratushnyak, Apr 22 2012

Examples

			For n = 15, a(15) = 37 because the 15th prime is 47 and the 16th is 53, which have binary representations of 101111 and 110101 respectively; the bitwise AND of these values is 100101 which is the binary representation of 37:
  101111
& 110101
--------
  100101
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Wikipedia, Bitwise operation

Crossrefs

Cf. A000040, A175329 (bitwise OR).

Cf. A129760 (bitwise AND of n and n-1).

Cf. A366550 (indices of ones).

Programs

Maple

read("transforms") ; A175330 := proc(n) ANDnos(ithprime(n),ithprime(n+1)) ; end proc: seq(A175330(n),n=1..60) ; # R. J. Mathar, Apr 15 2010
# second Maple program:
a:= n-> Bits[And](ithprime(n), ithprime(n+1)):
seq(a(n), n=1..70);  # Alois P. Heinz, Apr 15 2020

Mathematica

a[n_] := Prime[n]~BitAnd~Prime[n+1];
Array[a, 60] (* Jean-François Alcover, Jan 11 2021 *)

PARI

a(n) = bitand(prime(n), prime(n+1)); \\ Michel Marcus, Apr 16 2020

Scala

val prime: LazyList[Int] = 2 #:: LazyList.from(3).filter(i => prime.takeWhile {
   j => j * j <= i
}.forall {
   k => i % k != 0
})
(0 to 63).map(n => prime(n) & prime(n + 1)) // Alonso del Arte, Apr 18 2020

Extensions

More terms from R. J. Mathar, Apr 15 2010