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A154528 Composites k such that (smallest digit of k) + (multiplicity of smallest digit of k) is an even composite. 1

%I #15 Jul 19 2023 15:22:59

%S 9,22,34,35,36,38,39,44,56,57,58,63,65,66,75,78,85,87,88,93,95,111,

%T 224,225,226,228,232,242,252,262,272,282,292,322,333,344,345,346,348,

%U 354,355,356,357,358,364,365,366,368,369,374,375,376,377,378,384,385,386

%N Composites k such that (smallest digit of k) + (multiplicity of smallest digit of k) is an even composite.

%H Harvey P. Dale, <a href="/A154528/b154528.txt">Table of n, a(n) for n = 1..1000</a>

%e 9 (composite) is a term because 9 + 1 = 10 (even composite);

%e 22 (composite) is a term because 2 + 2 = 4 (even composite);

%e 34 (composite) is a term because 3 + 1 = 4 (even composite).

%p frequdig := proc(n,dig) local f,d ; f := 0 ; for d in convert(n,base,10) do if d = dig then f :=f+1; end if; end do; f ; end proc:

%p A054054 := proc(n) min(op(convert(n,base,10)) ) ; end proc:

%p for n from 1 to 500 do c := A002808(n) ; sdg := A054054(c) ; a := sdg +frequdig(c,sdg) ; if type(a,'even') and not isprime(a) then printf("%d,",c ) ; end if; end do: # _R. J. Mathar_, May 05 2010

%t ecQ[n_]:=Module[{idn=IntegerDigits[n],s,c},s=Min[idn];c=s+Count[idn,s];EvenQ[c]&&AllTrue[ {n,c},CompositeQ]]; Select[Range[400],ecQ] (* _Harvey P. Dale_, Jul 19 2023 *)

%Y Cf. A002808.

%K nonn,base

%O 1,1

%A _Juri-Stepan Gerasimov_, Jan 11 2009

%E Corrected (28 replaced with 38, 269 with 369) by _R. J. Mathar_, May 05 2010

%E Name and Example section edited by _Jon E. Schoenfield_, Feb 11 2019

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)