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).

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

Offset

1,2

Comments

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

Formula

n such that A000120(n) = A001222(n+1). - Franklin T. Adams-Watters, Aug 17 2012

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 ]))& ]
Select[Range[300], DigitCount[#, 2, 1]==PrimeOmega[#+1]&] (* Harvey P. Dale, Mar 11 2023 *)

Prog

(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)) ) } \\ Harry J. Smith, Sep 18 2009

Crossrefs

Cf. A000120, A001222, A058061, A064547.

Sequence in context: A111133 A279076 A076970 * A291927 A239497 A039850

Adjacent sequences: A064545 A064546 A064547 * A064549 A064550 A064551

Keyword

nonn

Author

Wouter Meeussen, Oct 09 2001

Status

approved