The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60, we have over 367,000 sequences, and we’ve crossed 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A065085 Smallest prime having alternating bit sum (A065359) equal to -n, or 0 if no such prime exists. 1
 3, 2, 43, 0, 683, 2731, 0, 43691, 174763, 0, 2796203, 44608171, 0, 715827881, 715827883, 0, 114532461227, 183251938027, 0, 2931494136491, 2932031007403, 0, 187647836990123, 748400914639531, 0, 11446649052900011, 45786596211600043, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Table of n, a(n) for n=0..27. W. Bomfim, Table of n, a(n) for n = 0..117 EXAMPLE The smallest number having alternating bit sum -n is (2/3)(4^n-1), which for n=4 is 170 = (10101010)2. The least odd number with alternating bit sum -4 is (10)2 || ( (10101010)2 + (1)2 ) = 683, which is prime, so a(4) = 683. - Washington Bomfim, Jan 27 2011 MATHEMATICA f[n_] := Plus @@ (-(-1)^Range[Floor[Log2@n + 1]] Reverse@ IntegerDigits[n, 2]); a = Table[ f[ Prime[n]], {n, 1, 10^6} ]; b = Table[0, {12} ]; Do[ If[ a[[n]] < 1 && b[[ -a[[n]] + 1]] == 0, b[[ -a[[n]] + 1]] = Prime[n]], {n, 1, 10^6} ]; b PROG (PARI)II()={i = (2/3)*(4^n-1) + 1 + 2^(2*n+1); if(isprime(i), return(1)); return(0)}; III()={w = 2^(2*n+3); for(j=1, n+1, i += w; w /= 4; i -= w; if(isprime(i), return(1))); return(0)}; IV()={i+=6; if(isprime(i), return(1)); w=4; for(j=1, n, i -= w; w*=4; i+=w; if(isprime(i), return(1))); return(0)}; V()={i += 2^(2*n+4) - 2^(2*n+2); if(isprime(i), return(1)); w = i + 2^(2*n+5) - 2^(2*n+4); i = w - 2^(2*n+3) - 2^(2*n+1); if(isprime(i), return(1)); w = 2^(2*n+1); for(j=1, n, i += w; w /= 4; i -= w; if(isprime(i), return(1) )); return(0)}; print("0 3"); print("1 2"); for(n=2, 117, if(II(), print(n, " ", i), if(III(), print(n, " ", i), if(IV(), print(n, " ", i), if(V(), print(n, " ", i), if(n%3==0, print(n, " 0"), print(n, " not found."))))))) \\ Washington Bomfim, Feb 06 2011 CROSSREFS Cf. A065359, A020988. Sequence in context: A096057 A179984 A260888 * A321169 A093398 A002680 Adjacent sequences: A065082 A065083 A065084 * A065086 A065087 A065088 KEYWORD nonn AUTHOR Robert G. Wilson v, Nov 09 2001 EXTENSIONS a(13)-a(27) from Washington Bomfim, Jan 27 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 09:50 EST 2023. Contains 367517 sequences. (Running on oeis4.)