A071117 Numbers k such that the sum of the first k digits of the decimal expansion of e is prime.
1, 7, 8, 10, 18, 24, 38, 42, 52, 54, 64, 100, 107, 112, 113, 114, 135, 144, 145, 150, 151, 159, 162, 172, 177, 184, 189, 196, 197, 202, 213, 214, 223, 228, 230, 232, 238, 239, 240, 252, 255, 264, 267, 272, 278, 283, 302, 314, 315, 316, 332, 338, 366, 367, 374
Offset: 1
Examples
7 is a term because 2+7+1+8+2+8+1 = 29.
Programs
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Mathematica
a = First[ RealDigits[ N[ E, 400]]]; Do[ If[ PrimeQ[Plus @@ Take[a, n]], Print[n]], {n, 1, 375}]