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A117711 Pentagonal numbers for which both the sum of the digits and the product of the digits are pentagonal numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 30 10:34 EST 2023. Contains 359943 sequences. (Running on oeis4.)