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 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 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: A321517 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

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Last modified January 20 16:46 EST 2019. Contains 319335 sequences. (Running on oeis4.)