Wednesday, September 10, 2025

The three-millionth term of A157711

The sum of the first 3103 prime counts of A383675 is 2998833. The sum of the first 3104 prime counts is 3000310. Hence, the three-millionth term of A157711 is a 3104-digit integer:

2998834 10^3103+10^74+10^52+1
2998835 10^3103+10^111+10^95+1
2998836 10^3103+10^113+10^75+1
2998837 10^3103+10^151+10^27+1
2998838 10^3103+10^153+10^97+1
...
2999995 10^3103+10^2746+10^334+1
2999996 10^3103+10^2746+10^1064+1
2999997 10^3103+10^2746+10^1168+1
2999998 10^3103+10^2746+10^2436+1
2999999 10^3103+10^2747+10^21+1
3000000 10^3103+10^2747+10^859+1
3000001 10^3103+10^2747+10^2187+1
3000002 10^3103+10^2749+10^445+1
3000003 10^3103+10^2749+10^515+1
3000004 10^3103+10^2749+10^575+1
3000005 10^3103+10^2751+10^1427+1
...
3000306 10^3103+10^3099+10^915+1
3000307 10^3103+10^3099+10^2509+1
3000308 10^3103+10^3100+10^2160+1
3000309 10^3103+10^3101+10^3091+1
3000310 10^3103+10^3102+10^388+1

A157711(1*10^6) = 10^1793+10^673+10^615+1 [June 19]
A157711(2*10^6) = 10^2535+10^1160+10^398+1 [July 21]
A157711(3*10^6) = 10^3103+10^2747+10^859+1 (above)
A157711(4*10^6) ~ 10^3582 [this will take a while]