Find the position of your birthday in the digits of Pi. Increase the number of digits, if necessary, to find the sequence:
SequencePosition[First[RealDigits[Pi, 10, 1000000]], {1, 2, 3, 4, 5}]
The end of the first occurrence of the sequence is 49,707. Get the first 49,707 digits of Pi and give it the name digits:
digits = First[RealDigits[Pi, 10, 49707]];
49,707 digits are way too many to print, so instead make an abbreviated form.
This gives the first 100 digits:
digits[[1 ;; 100]]
This gives the last 100 digits (-1 means the last digit, -100 means the 100th-from-last digit):
digits[[-100 ;; -1]]
Row formats a list of objects without the braces, commas, and quotation marks—for example:
Row[{"The ", 5, "th prime is ", 11, "."}]
Use Row to show the first 100 digits, an ellipsis (...), and the last 100 digits. Flatten flattens out the sublists of digits:
Row[Flatten[{digits[[1 ;; 100]], "...", digits[[-100 ;; -1]]}]]
Restore the decimal point by omitting the first digit and supplying the missing 3 and decimal point explicitly:
Row[Flatten[{"3.", digits[[2 ;; 100]], "...", digits[[-100 ;; -1]]}]]
This code is essentially what was implemented to make the Wolfram My Pi Day site.
digits = First[RealDigits[Pi, 10, 49707]];
Row[Flatten[{"3.", digits[[2 ;; 100]], "...", digits[[-100 ;; -1]]}]]