# [seqfan] Re: Sum of primes - 10^9 increment

Robert G. Wilson, v rgwv at rgwv.com
Sat Feb 21 07:57:26 CET 2009

Dear Jacques,

Prime Counts:

A046731  Sum of primes < 10^n. (which is the first term of the sequences
below:
0, 17, 1060, 76127, 5736396, 454396537, 37550402023, 3203324994356,
279209790387276, 24739512092254535, 2220822432581729238,
201467077743744681014, 18435588552550705911377,
1699246443377779418889494, 157589260710736940541561021,
14692398516908006398225702366, 1376110854313351899159632866552,
129408626276669278966252031311350, 12212914292949226570880576733896687,
1156251260549368082781614413945980126,
109778913483063648128485839045703833541,
10449550362130704786220283253063405651965

A034387 Sum of primes < n: 0, 2, 5, 5, 10, 10, 17, 17, 17, 17, 28, 28,
41, 41, 41
Sum of primes < 10*n:      17, 77, 129, 197, 328, 440, 568, 791, 963, 1060
Sum of primes < 10^2*n:    1060, 4227, 8275, 13887, 21536, 29296, 39612,
50078, 62797, 76127
Sum of primes < 10^3*n:    76127, 277050, 593823, 1013507, 1548136,
2174734, 2935471, 3738566, 4673790, 5736396
Sum of primes < 10^4*n:    5736396, 21171191, 45675864, 79170666,
121013308, 171848738, 228890418, 296488208, 370927314, 454396537
Sum of primes < 10^5*n:    454396537, 1709600813, 3709507114,
6458901531, 9914236195, 14071826345, 18910286312, 24465663438,
30689332265, 37550402023
Sum of primes < 10^6*n:    37550402023, 142913828922, 312471072265,
544501644261, 838596693108, 1192390967254, 1607061425171, 2080483502248,
2613521583098, 3203324994356
Sum of primes < 10^7*n:    3203324994356, 12272577818052,
26942805919966, 47088408550139, 72619548630277, 103468900363400,
139601928199359, 180946446237951, 227485624300931, 279209790387276
Sum of primes < 10^8*n:    279209790387276, 1075207199997334,
2367646772295462, 4146437503168147, 6404774487532576, 9137303389808024,
12340337443955708, 16010026481858292, 20143329357815162, 24739512092254535
Sum of primes < 10^9*n:    24739512092254535,
Sum of primes < 10^10*n:   2220822432581729238, thereafter every tenth
term above.

Between the two of us we should be able to quickly assemble a dozen
sequence which put all of this in order. If you
are willing I would like to jointly submit these twelve sequences with
you. Each should have a hyper-link to a file
which contains a 1000 terms.

Sincerely yours,
Robert G. "Bob" Wilson, v
Ph.D.,  ATP / CF & GI
an associate editor of the OEIS.

Jacques Tramu wrote:

>Hi SeqFans,
>Let sp(n) = Sum of primes <=n
>
>For some reason (Carlos Rivera), I had to build and record the sequence :
>
>a[i] = sp(i * 10^9)    i=1,..,1000
>
>a[1] = 24739512092254535
>...
>a[10] = 2220822432581729238
>...
>a[1000] = 18435588552550705911377
>
>Is this sequence of any interest to the OEIS ?
>
>
>-------------------------------------
>http://www.echolalie.com/gbnums
>-------------------------------------
>
>
>
>_______________________________________________
>
>Seqfan Mailing list - http://list.seqfan.eu/
>
>
>