Sunday, June 07, 2026

The six-millionth term of A157711

The sum of the first 4388 prime counts of A383675 is 5997438. The sum of the first 4389 prime counts is 6000600. Hence, the six-millionth term of A157711 is a 4389-digit integer:

5997439 10^4388+10^31+10^26+1
5997440 10^4388+10^84+10^57+1
5997441 10^4388+10^86+10^4+1
5997442 10^4388+10^109+10^14+1
5997443 10^4388+10^116+10^4+1
...
5999995 10^4388+10^3965+10^1276+1
5999996 10^4388+10^3965+10^1598+1
5999997 10^4388+10^3965+10^3206+1
5999998 10^4388+10^3966+10^1952+1
5999999 10^4388+10^3967+10^1856+1
6000000 10^4388+10^3968+10^1845+1
6000001 10^4388+10^3968+10^3913+1
6000002 10^4388+10^3970+10^1513+1
6000003 10^4388+10^3970+10^3499+1
6000004 10^4388+10^3971+10^744+1
6000005 10^4388+10^3971+10^1820+1
...

A157711(1*10^6) = 10^1793+10^673+10^615+1 [2025 June 19]
A157711(2*10^6) = 10^2535+10^1160+10^398+1 [2025 July 21]
A157711(3*10^6) = 10^3103+10^2747+10^859+1 [2025 September 10]
A157711(4*10^6) = 10^3583+10^3040+10^2776+1 [2025 December 7]
A157711(5*10^6) = 10^4006+10^2673+10^876+1 [2026 February 14]
A157711(6*10^6) = 10^4388+10^3968+10^1845+1 (above)
A157711(7*10^6) ~ 10^4740

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

A383675 to n=4400; max=(4361,3555) [updated June 7]  click to enlarge

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