login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A259670 Numbers n with the property that it is possible to write the base 2 expansion of n as concat(a_2,b_2), with a_2>0 and b_2>0 such that, converting a_2 and b_2 to base 10 as a and b, we have antisigma(a) + antisigma(b) = n. 0
50, 77, 179, 346, 347, 550, 1758, 1909, 9205, 27884, 30660, 37354, 52019, 88052, 107974, 131590, 164413, 232447, 295682, 326133, 328491, 1494561, 1541005, 1541851 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..24.

EXAMPLE

50 in base 2 is 110010. If we take 110010 = concat(1100,10) then 1100 and 10 converted to base 10 are 12 and 2. Finally 12*13/2 - sigma(12) + 2*3/2 - sigma(2) = 78 - 28 + 3 - 3 = 50.

179 in base 2 is 1001101. If we take 1001101 = concat(11100,1) then 11100 and 1 converted to base 10 are 5 and 19. Finally 5*6/2 - sigma(5) + 19*20/2 - sigma(19) = 15 - 6 + 190 - 20 = 179.

MAPLE

with(numtheory): P:=proc(q) local a, b, c, j, k, n;

for n from 1 to q do c:=convert(n, binary, decimal);

j:=0; for k from 1 to ilog10(c) do

a:=convert(trunc(c/10^k), decimal, binary);

b:=convert((c mod 10^k), decimal, binary);

if a*b>0 then if a*(a+1)/2-sigma(a)+b*(b+1)/2-sigma(b)=n then print(n);

break; fi; fi; od; od; end: P(10^9);

MATHEMATICA

f[n_] := Block[{d = IntegerDigits[n, 2], len = IntegerLength[n, 2], k}, ReplaceAll[Reap[Do[k = {FromDigits[Take[d, i], 2], FromDigits[Take[d, -(len - i)], 2]}; If[! MemberQ[k, 0], Sow@ k], {i, 1, len - 1}]], {} -> {1}][[-1, 1]]]; Select[Range@ 100000, MemberQ[Total /@ (# (# + 1)/2 - DivisorSigma[1, #] &) /@ f@ #, #] &] (* Michael De Vlieger, Jul 03 2015 *)

CROSSREFS

Cf. A024816, A253824, A253825, A258813, A258843, A258844.

Sequence in context: A071366 A045165 A261286 * A138381 A224551 A262149

Adjacent sequences:  A259667 A259668 A259669 * A259671 A259672 A259673

KEYWORD

nonn,base,more

AUTHOR

Paolo P. Lava, Jul 03 2015

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 04:04 EDT 2018. Contains 316431 sequences. (Running on oeis4.)