A117527 Cumulative sums of int(prime*e) which are primes.
5, 13, 109, 641, 757, 4007, 5387, 7901, 9349, 11467, 23297, 33503, 42193, 57139, 76343, 100213, 209597, 252583, 261631, 373621, 424231, 432287, 503593, 507961, 618593, 699427, 791489, 825389, 895243, 943837, 1212917, 1455901, 1573577
Offset: 1
Examples
The 4th cumulative sum of integer products is 641, prime.
Programs
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Mathematica
Select[Accumulate[Floor[E*Prime[Range[500]]]],PrimeQ] (* Harvey P. Dale, Mar 27 2025 *)
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UBASIC
10 Ct=1 20 B=nxtprm(B) 22 E=#e 30 C=int(B*E) 40 D=D+C 41 print Ct,B,C,D 50 if D=prmdiv(D) then print D:stop 55 Ct=Ct+1 60 goto 20
Formula
Beginning with the first prime, multiply by e, take integer, repeat, adding integer sums until a cumulative prime sum occurs. On the first prime, 2, the integer product is 5, prime. Continue to next integer product, add, until the next prime sum, 13.
Comments