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A175333 a(n) is the smallest prime such that (binary a(n)) OR (binary prime(n)) is one less than a power of 2. 1
3, 2, 2, 2, 5, 2, 31, 13, 11, 2, 2, 31, 23, 23, 17, 11, 5, 2, 61, 59, 127, 53, 47, 47, 31, 31, 29, 23, 19, 31, 2, 127, 127, 127, 107, 107, 103, 127, 89, 83, 79, 79, 67, 127, 59, 59, 47, 37, 29, 31, 23, 17, 31, 5, 8191, 251, 251, 241, 239, 239, 229, 223, 223, 223, 199, 199 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

By a(n) "OR" prime(n), OR the respective digits, reading right to left, of a(n) and the n-th prime written in binary.

Each digit of binary a(n) OR'ed with the respective (reading right to left) digit of binary prime(n) is 1.

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

19, the 8th prime, in binary is 10011. The smallest number that when written in binary and OR'ed with 10011, then it is a power of 2 minus 1, is 12 (1100 in binary). But 12 is not a prime. The next larger number that works, which is a prime, is 13 (1101 in binary). OR'ing the respective digits of 10011 and 01101 (with appropriate leading 0), from right to left, is: 1 OR 1 = 1; 1 OR 0 = 1; 0 OR 1 = 1; 0 OR 1 = 1; and 1 OR 0 = 1. Since all pairs of respective digits OR'ed equal 1 (and the resulting binary number represents a power of 2 minus 1), then a(8) = 13.

MAPLE

read("transforms");

A175333 := proc(n) local i, p, a ; for i from 1 do p := ithprime(i) ; a := ORnos(p, ithprime(n)) +1 ; if numtheory[factorset](a) = {2} then return p; end if; end do: end proc:

seq(A175333(n), n=1..80) ; # R. J. Mathar, May 28 2010

CROSSREFS

Sequence in context: A024703 A102845 A064126 * A130845 A134653 A090207

Adjacent sequences:  A175330 A175331 A175332 * A175334 A175335 A175336

KEYWORD

base,nonn

AUTHOR

Leroy Quet, Apr 14 2010

EXTENSIONS

More terms from R. J. Mathar, May 28 2010

STATUS

approved

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Last modified June 15 17:43 EDT 2019. Contains 324142 sequences. (Running on oeis4.)