A117711 Pentagonal numbers for which both the sum of the digits and the product of the digits are pentagonal numbers.

0, 1, 5, 6501, 8400, 10542, 10795, 18760, 21540, 32340, 45850, 50142, 50692, 55200, 60501, 72490, 91390, 104412, 127750, 160230, 170185, 179401, 208507, 239800, 250717, 272001, 273280, 333940, 346801, 400675, 429070, 442002, 520087, 536107, 552370, 602617, 637330

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

6501 is a pentagonal number whose sum of digits 6+5+0+1 = 12 and product of digits 6*5*0*1 = 0 are both pentagonal.

Mathematica

sod[n_] := Plus @@ IntegerDigits[n]; pod[n_] := Times @@ IntegerDigits[n]; pentQ[n_] := n == 0 || IntegerQ[(Sqrt[24*n + 1] + 1)/6]; Select[Table[n*(3*n - 1)/2, {n, 0, 1000}], pentQ[sod[#]] && pentQ[pod[#]] &] (* Amiram Eldar, Feb 06 2021 *)

Crossrefs

Cf. A000326, A007953, A007954, A117053, A117064.

Sequence in context: A137694 A292334 A202156 * A203689 A116140 A243235

Adjacent sequences: A117708 A117709 A117710 * A117712 A117713 A117714

Keyword

base,nonn

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 13 2006

Extensions

Offset and data corrected by Amiram Eldar, Feb 06 2021

Status

approved