Martin Rees

The two-millionth term of OEIS sequence A157711

On Saturday, I updated my b-file and b-file plot at A383675 from 1200 to 2500 terms. The sum of those 2500 prime counts is 1945287, so I knew that I was within striking distance of two million terms of A157711. In fact, the sum of the first 2535 prime counts is 1999666, pretty much assuring that the two-millionth term of A157711 will be a 2536-digit integer:

1999667 10^2535+10^14+10^6+1
1999668 10^2535+10^65+10^51+1
1999669 10^2535+10^78+10^60+1
1999670 10^2535+10^91+10^33+1
1999671 10^2535+10^98+10^24+1
    ...
1999995 10^2535+10^1155+10^623+1
1999996 10^2535+10^1157+10^205+1
1999997 10^2535+10^1157+10^351+1
1999998 10^2535+10^1159+10^1095+1
1999999 10^2535+10^1160+10^50+1
2000000 10^2535+10^1160+10^398+1
2000001 10^2535+10^1161+10^341+1
2000002 10^2535+10^1162+10^442+1
2000003 10^2535+10^1162+10^536+1
2000004 10^2535+10^1162+10^652+1
2000005 10^2535+10^1163+10^561+1
    ...
2001288 10^2535+10^2532+10^146+1
2001289 10^2535+10^2532+10^424+1
2001290 10^2535+10^2532+10^1240+1
2001291 10^2535+10^2533+10^143+1
2001292 10^2535+10^2533+10^2529+1

A157711(1*10^6) = 10^1793+10^673+10^615+1
A157711(2*10^6) = 10^2535+10^1160+10^398+1 (above)
A157711(3*10^6) = (in a future blog, I'll guess ~10^3100)

I'll continue to update (here, until the next millionth is reached) my current plot of A383675:

A383675 to n=2536; max=(2457,1993) [updated July 21]  click to enlarge

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