A274620 - OEIS

A274620

If n^2 has an even number of digits, write n after the left half of the digits of n^2 and before the right half, otherwise if n^2 has 2t+1 digits, write n after the first t digits of n^2 and before the last t+1 digits.

11, 24, 39, 146, 255, 366, 479, 684, 891, 11000, 11121, 11244, 11369, 11496, 21525, 21656, 21789, 31824, 31961, 42000, 42141, 42284, 52329, 52476, 62525, 62676, 72729, 72884, 82941, 93000, 93161, 103224, 103389, 113456, 123525, 123696, 133769, 143844, 153921, 164000

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

In short, write n in the middle of n^2.

Portions of this sequence are sometimes given as puzzles.

REFERENCES

J. A. Reeds, Personal communication to N. J. A. Sloane, Jun 04 2016

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

EXAMPLE

4^2 = 16 so a(4) = 1.4.6 = 146.

19^2 = 361 so a(19) = 3.19.61 = 31961.

MATHEMATICA

nterms=100; Table[FromDigits[Flatten[Insert[d=IntegerDigits[n^2], IntegerDigits[n], Floor[Length[d]/2]+1]]], {n, nterms}] (* Paolo Xausa, Nov 24 2021 *)

PROG

(Python)

def a(n):

ss = str(n*n)

t = len(ss)//2

return int(ss[:t] + str(n) + ss[t:])

print([a(n) for n in range(1, 41)]) # Michael S. Branicky, Nov 24 2021

CROSSREFS

Cf. A053061, A055436.

Sequence in context: A061043 A349487 A098603 * A053061 A055820 A334597

Adjacent sequences: A274617 A274618 A274619 * A274621 A274622 A274623

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane, Jul 03 2016

STATUS

approved