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A139565 Squares without a 0 digit and whose sum of digits minus 1 and product of digits plus 1 are both squares. 1
64, 187489, 529984, 2982529, 6165289, 45819361, 55279225, 59613841, 85914361, 89151364, 114297481, 118417924, 181252369, 183196225, 223981156, 231861529, 411197284, 446519161, 582691321, 599221441, 644195161, 876811321, 941814721 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Travis Scholl, Table of n, a(n) for n = 1..122

Matthew M. Conroy, Worst proof ever

EXAMPLE

64 -> 6+4-1=9 (3) and 6*4+1=25 (5).

187489 -> 1+8+7+4+8+9-1=36 (6) and 1*8*7*4*8*9+1=16129 (127).

MAPLE

P:=proc(n) local i, k, w, y; for i from 1 by 1 to n do w:=0; k:=i^2; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; w:=w-1; y:=1; k:=i^2; while k>0 do y:=y*(k-(trunc(k/10)*10)); k:=trunc(k/10); od; y:=y+1; if w=trunc(sqrt(w))^2 and y=trunc(sqrt(y))^2 and y>1 then print(i^2); fi; od; end: P(50000);

PROG

(PARI) isok(n) = issquare(n) && (d=digits(n)) && vecmin(d) && issquare(vecsum(d)-1) && issquare(prod(k=1, #d, d[k])+1); \\ Michel Marcus, Apr 09 2016

CROSSREFS

Sequence in context: A227660 A029753 A036533 * A214388 A016938 A017010

Adjacent sequences:  A139562 A139563 A139564 * A139566 A139567 A139568

KEYWORD

easy,nonn,base

AUTHOR

Paolo P. Lava and Giorgio Balzarotti, Jun 11 2008

EXTENSIONS

Name clarified by Travis Scholl, Apr 09 2016

STATUS

approved

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Last modified July 4 22:15 EDT 2020. Contains 335449 sequences. (Running on oeis4.)