Numbers 240,000,000,000s

240,634,397,025

[Math.]  Sum of the first 990 cube numbers:

13+…+9903 = 240,634,397,025 = (1+…+990)2 = 490,5452.

241,607,639,296

[Math.]  Sum of the first 991 cube numbers:

13+…+9913 = 241,607,639,296 = (1+…+991)2 = 491,5362.

242,583,830,784

[Math.]  Sum of the first 992 cube numbers:

13+…+9923 = 242,583,830,784 = (1+…+992)2 = 492,5282.

243,394,471,320

[Math.]  Two consecutive sums of consecutive square numbers:

243,394,471,320 = 410412+…+411842 = 411852+…+413272.

243,562,977,441

[Math.]  Sum of the first 993 cube numbers:

13+…+9933 = 243,562,977,441 = (1+…+993)2 = 493,5212.

244,242,535,681

[Math.]    (1+2+…+37)4 = [(15+25+…+375)+(17+27+…+377)]/2.

244,545,085,225

[Math.]  Sum of the first 994 cube numbers:

13+…+9943 = 244,545,085,225 = (1+…+994)2 = 494,5152.

245,530,160,100

[Math.]  Sum of the first 995 cube numbers:

13+…+9953 = 245,530,160,100 = (1+…+995)2 = 495,5102.

246,518,208,036

[Math.]  Sum of the first 996 cube numbers:

13+…+9963 = 246,518,208,036 = (1+…+996)2 = 496,5062.

246,963,938,824

[Math.]  62743 = 246,963,938,824 has each of its digits occurring twice.

247,509,235,009

[Math.]  Sum of the first 997 cube numbers:

13+…+9973 = 247,509,235,009 = (1+…+997)2 = 497,5032.

248,503,247,001

[Math.]  Sum of the first 998 cube numbers:

13+…+9983 = 248,503,247,001 = (1+…+998)2 = 498,5012.

249,499,251,001

[Math.]  (Sequence of numbers 49…949…9).

249,499,251,001 = (249+499251–001)2 = 4994992.

249,500,250,000

[Math.]   (Sequence of numbers 49…950…0 and 50…050…0).

249,500,250,000 = (249,500+250,000)2 = 499,5002 and 250,500,250,000 = (250,500+250,000)2 = 500,5002 and 499,500+500,500 = 1,000,000.

249,500,250,000

[Math.]  Sum of the first 999 cube numbers:

13+…+9993 = 250,500,250,000 = (1+…+999)2 = 499,5002.

249,999,500,000

[Math.]   (Sequence of numbers 49…950…0 and 50…050…0).

249,999,500,000,250,000,000,000 = (249,999,500,000+250,000,000,000)2

= 499,999,500,0002 and

25,000,500,002,500,000,000 = (250,000,500,000+250,000,000,000)2

= 500,000,500,0002 and 499,999,500,000+500,000,500,000 = 1,000,000,000,000.

249,999,999,997

[Math.]  The number of 0’s that the factorial of 1 trillion ends in.

249,999,999,997 = [[1,000,000,000,000/5]]+…+[[1,000,000,000,000/517]],

where [[x]] is the floor function of x, i.e. which is the largest integer less than x (or the integral part of x).