A117709 Pentagonal numbers for which the sum of the digits is also a pentagonal number.

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

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