The Astronomer's Telescope

The Story: At the Vainu Bappu Observatory in the Javadi Hills of Tamil Nadu, a young astronomer named Selvi is running an all-night observation session. She is tracking a sequence of pulsing signals from a distant star — the signals arrive in a mathematical pattern. She records the first several values in her notebook: 2, 5, 11, 23, 47... She stares at the sequence. There is clearly a pattern — each number seems to be generated from the previous one — but she cannot immediately see it. Her colleague, Dr. Basu, peers over her shoulder. 'Find the pattern,' he says. 'Then tell me the next three values. And then tell me whether the 20th term of the sequence is prime.' Selvi taps her pen against the desk and looks at the numbers again. The Challenge: Identify the rule governing the sequence 2, 5, 11, 23, 47. Find the next three terms. Determine a formula for the nth term. Then determine whether the 20th term is prime.