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A080438 Smallest square obtained by inserting one or more digits between every pair of consecutive digits of n^2. 0
1, 4, 9, 196, 225, 3136, 4489, 6084, 841, 10000, 10201, 10404, 10609, 12996, 27225, 27556, 27889, 39204, 39601, 40000, 40401, 40804, 54289, 54756, 616225, 617796, 71289, 71824, 89401, 90000, 90601, 10036224, 1108809, 10150596, 1525225, 1920996 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If n^2 has k digits, there are (k-1) places where digit insertion takes place, and a(n) contains at least 2k-1 digits.

LINKS

Table of n, a(n) for n=1..36.

PROG

(PARI) { a(n) =  m=Vec(Str(n^2)); r=0; k=#m-1; while(!r, forvec(w=vector(#m-2, i, [1, k-1]), v=vector(#w+1, i, if(i<=#w, w[i], k)-if(i>1, w[i-1])); forvec(u=vector(#v, i, [0, 10^v[i]-1]), t=m[1]; for(i=1, #v, if(#Str(u[i])<v[i], t=concat(t, concat(vector(v[i]-#Str(u[i]), j, "0"))); ); t=concat([t, Str(u[i]), m[i+1]]); ); t=eval(t); if( issquare(t) && (r==0 || t<r), r=t); ); , 2); k++; ); r } \\ Max Alekseyev, Feb 11 2012

CROSSREFS

Cf. A080436, A080437.

Sequence in context: A318616 A029738 A067072 * A029999 A006280 A290158

Adjacent sequences:  A080435 A080436 A080437 * A080439 A080440 A080441

KEYWORD

base,nonn

AUTHOR

Amarnath Murthy, Feb 21 2003

EXTENSIONS

More terms from Max Alekseyev, Feb 11 2012

STATUS

approved

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Last modified November 22 16:31 EST 2019. Contains 329396 sequences. (Running on oeis4.)