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 A117709 Pentagonal numbers for which the sum of the digits is also a pentagonal number. 0
 0, 1, 5, 651, 1335, 2262, 3432, 3577, 6501, 8400, 8626, 10542, 10795, 15862, 18760, 21540, 25285, 28912, 32340, 32782, 45850, 50142, 50692, 55200, 60501, 72490, 91390, 98945, 104412, 112477, 127750, 135751, 152482, 160230, 170185, 179401 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..35. EXAMPLE 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. MAPLE 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 MATHEMATICA With[{pnts=Table[(n(3n-1))/2, {n, 0, 500}]}, Select[pnts, MemberQ[ pnts, Total[ IntegerDigits[#]]]&]] (* Harvey P. Dale, Sep 25 2018 *) CROSSREFS Cf. A000326. Sequence in context: A142535 A203475 A203701 * A185820 A332165 A133750 Adjacent sequences: A117706 A117707 A117708 * A117710 A117711 A117712 KEYWORD base,nonn AUTHOR Luc Stevens (lms022(AT)yahoo.com), Apr 13 2006 STATUS approved

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Last modified June 22 00:43 EDT 2024. Contains 373561 sequences. (Running on oeis4.)