A181791
Numbers with pandigital biperiod squares.
Original entry on oeis.org
428571428571428571429, 571428571428571428572, 857142857142857142858, 363636363636363636363636363636364, 454545454545454545454545454545455, 545454545454545454545454545454546, 636363636363636363636363636363637
Offset: 1
- R. Ondrejka, Problem 1130: Biperiod Squares, Journal of Recreational Mathematics, Vol. 14:4 (1981-82), 299. Solution by F. H. Kierstead, Jr., JRM, Vol. 15:4 (1982-83), 311-312.
A107677
Numbers A such that the square of concatenation AA is of form NNMM.
Original entry on oeis.org
8, 89, 98, 406, 593, 998, 4445, 4544, 5455, 5554, 9899, 9998, 34687, 44443, 55556, 65312, 90242, 99998, 219374, 285713, 286714, 296297, 297296, 340066, 362636, 363637, 374219, 416989, 583010, 625780, 636362, 637363, 659933, 702703, 703702
Offset: 1
593 is in the sequence because we have 593593^2 = 352352649649; 998 is in the sequence since 998998^2 = 997997004004 (M has two leading zeros); 219374 is in the sequence since 219374219374^2 = 48125048125951876951876 (N has one leading zero).
A115530
Numbers k such that k^2 is the concatenation of two numbers 2*m and m.
Original entry on oeis.org
5714285714285714286, 8571428571428571429, 11428571428571428572, 465116279069767441860465116279070, 511627906976744186046511627906977, 558139534883720930232558139534884, 604651162790697674418604651162791
Offset: 1
5714285714285714286^2 = 3265306122448979592_1632653061224489796.
A115532
Numbers k such that k^2 is the concatenation of two numbers m and 3*m.
Original entry on oeis.org
2857142857142857142857142857142858, 4285714285714285714285714285714287, 5714285714285714285714285714285716, 19354838709677419354838709677419354838709677419354838709678
Offset: 1
A115533
Numbers k such that the concatenation of 3*k with k gives a square.
Original entry on oeis.org
24489796, 55102041, 97959184, 15976331361, 28402366864, 44378698225, 63905325444, 86982248521, 24489795918367346938775510204081632653061224489796
Offset: 1
73469388_24489796 = 85714286^2.
A115534
Numbers k such that k^2 is the concatenation of two numbers 3*m and m.
Original entry on oeis.org
85714286, 128571429, 171428572, 69230769231, 92307692308, 115384615385, 138461538462, 161538461539, 85714285714285714285714285714285714285714285714286
Offset: 1
85714286^2 = 73469388_24489796.
A115535
Numbers k such that the concatenation of k with 4*k gives a square.
Original entry on oeis.org
25721, 28836, 32129, 35600, 39249, 43076, 47081, 51264, 55625, 60164, 64881, 69776, 74849, 80100, 85529, 91136, 96921, 102884, 109025, 115344, 121841, 128516, 135369, 142400, 149609, 156996, 164561, 172304, 180225, 188324, 196601, 205056
Offset: 1
A115536
Numbers k such that the square of k is the concatenation of two numbers m and 4*m.
Original entry on oeis.org
160378, 169812, 179246, 188680, 198114, 207548, 216982, 226416, 235850, 245284, 254718, 264152, 273586, 283020, 292454, 301888, 311322, 320756, 330190, 339624, 349058, 358492, 367926, 377360, 386794, 396228, 405662
Offset: 1
A115537
Numbers k such that the concatenation of 4*k with k gives a square.
Original entry on oeis.org
17728531856, 27700831025, 39889196676, 54293628809, 70914127424, 89750692521, 32653061224489796, 73469387755102041, 1245674740484429065743944636678200692041522491349481
Offset: 1
70914127424_17728531856 = 84210526316^2.
A115538
Numbers k such that k^2 is the concatenation of two numbers 4*m and m.
Original entry on oeis.org
84210526316, 105263157895, 126315789474, 147368421053, 168421052632, 189473684211, 114285714285714286, 171428571428571429, 7058823529411764705882352941176470588235294117647059
Offset: 1
84210526316^2 = 70914127424_17728531856.
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