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%I #10 Feb 03 2019 19:08:36
%S 0,1,5,651,1335,2262,3432,3577,6501,8400,8626,10542,10795,15862,18760,
%T 21540,25285,28912,32340,32782,45850,50142,50692,55200,60501,72490,
%U 91390,98945,104412,112477,127750,135751,152482,160230,170185,179401
%N Pentagonal numbers for which the sum of the digits is also a pentagonal number.
%e 651 is in the sequence because it is a pentagonal number and the sum of its digits 6 + 5 + 1 = 12 is also a pentagonal number.
%p a:=proc(n) local P,s: P:=convert(n*(3*n-1)/2,base,10): s:=add(P[j],j=1..nops(P)): if n=0 then 0 elif type((1+sqrt(1+24*s))/6,integer) then n*(3*n-1)/2 fi end: seq(a(n),n=0..350); # _Emeric Deutsch_, Apr 15 2006
%t With[{pnts=Table[(n(3n-1))/2,{n,0,500}]},Select[pnts,MemberQ[ pnts, Total[ IntegerDigits[#]]]&]] (* _Harvey P. Dale_, Sep 25 2018 *)
%Y Cf. A000326.
%K base,nonn
%O 0,3
%A Luc Stevens (lms022(AT)yahoo.com), Apr 13 2006