|
Search: id:A064548
|
|
|
| A064548 |
|
Numbers n for which the sum of the binary digits (or count of 1-bits) equals the sum of the prime exponents of n+1 (or the factor-count of n+1). |
|
+0
3
|
|
| 1, 2, 3, 4, 5, 7, 9, 11, 15, 16, 19, 20, 23, 24, 26, 31, 33, 34, 39, 41, 44, 47, 48, 49, 53, 63, 67, 68, 69, 74, 79, 83, 89, 95, 97, 98, 99, 104, 107, 127, 132, 135, 137, 139, 144, 146, 149, 152, 159, 160, 164, 167, 179, 191, 194, 195, 197, 199, 209, 215, 242, 255
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
This sequence becomes rare for large n: 15 values between 100000 and 101024 and none between 1000000 and 1001024
|
|
LINKS
|
Harry J. Smith, Table of n, a(n) for n=1,...,1000
|
|
EXAMPLE
|
8 is absent since 8 in binary is (1000) with sum=1, while (8+1) has 2 factors.
|
|
MATHEMATICA
|
Select[ Range[ 1024 ], DigitCount[ #, 2, 1 ]===(Plus@@(Last/@FactorInteger[ #+1 ]))& ]
|
|
PROGRAM
|
(PARI) SumD(x)= { local(s); s=0; while (x>9, s+=x-10*(x\10); x\=10); return(s + x) } baseE(x, b)= { local(d, e, f); e=0; f=1; while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=10); return(e) } { n=0; for (m=1, 10^9, s=SumD(baseE(m, 2)); f=factor(m + 1)~; e=0; for (i=1, length(f), e+=f[2, i]; if (e>s, break)); if (s==e, write("b064548.txt", n++, " ", m); if (n==1000, break)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 18 2009]
|
|
CROSSREFS
|
A058061.
Cf. A064547.
Sequence in context: A161306 A111133 A076970 this_sequence A039850 A033100 A030741
Adjacent sequences: A064545 A064546 A064547 this_sequence A064549 A064550 A064551
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Wouter Meeussen (wouter.meeussen(AT)pandora.be), Oct 09 2001
|
|
|
Search completed in 0.002 seconds
|
