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A198097 n such that  d(1)*1! + d(2)*2! + ... + d(k)*k! is a perfect square, where d(i) are the decimal digits of n. 1
1, 4, 9, 10, 14, 21, 27, 33, 40, 46, 52, 65, 71, 79, 84, 90, 98, 100, 104, 108, 111, 133, 137, 140, 162, 166, 191, 195, 210, 212, 225, 241, 249, 254, 270, 278, 283, 301, 323, 327, 330, 352, 356, 381, 385, 400, 402, 415, 431, 439, 444, 460, 468, 473, 497, 513 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A198095 is included in this sequence.

If n is in the sequence, then so is 10*n. - Robert Israel, Aug 16 2020

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

137 is in the sequence because 1*1! + 3*2! + 7*3! = 1 + 6 + 42 = 7^2.

MAPLE

for n from 1 to 520 do :l:=length(n):n0:=n:s:=0:for m from l by -1  to 1 do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v :s:=s+u*m!:od: z:=sqrt(s):if  z=floor(z) then  printf(`%d, `, n):else fi:od:

# Simpler:

filter:= proc(n)

  local L, k;

  L:= convert(n, base, 10);

  issqr(add(L[-k]*k!, k=1..nops(L)))

end proc:

select(filter, [$1..1000]); # Robert Israel, Aug 16 2020

CROSSREFS

Cf. A198095, A198044.

Sequence in context: A010426 A243170 A054294 * A157908 A064973 A133764

Adjacent sequences:  A198094 A198095 A198096 * A198098 A198099 A198100

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Oct 21 2011

STATUS

approved

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Last modified October 17 21:17 EDT 2021. Contains 348065 sequences. (Running on oeis4.)