A139565 Squares without a 0 digit and whose sum of digits minus 1 and product of digits plus 1 are both squares.

64, 187489, 529984, 2982529, 6165289, 45819361, 55279225, 59613841, 85914361, 89151364, 114297481, 118417924, 181252369, 183196225, 223981156, 231861529, 411197284, 446519161, 582691321, 599221441, 644195161, 876811321, 941814721

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