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

Author

Enoch Haga, Mar 25 2006

Keywords

• easy
• nonn

Comments

Sometimes prime integer sums occur with consecutive primes, as 1601*e and 1607*e.

Examples

			The 4th cumulative sum of integer products is 641, prime.
		

Crossrefs

Cf. A117528 A117503.

Programs

Mathematica

Select[Accumulate[Floor[E*Prime[Range[500]]]],PrimeQ] (* Harvey P. Dale, Mar 27 2025 *)

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.