A317488 a(n) is the position of the first occurrence of n > a(n-1) after the decimal point in e = 2.71828182845904523...
2, 4, 17, 25, 29, 31, 36, 86, 107, 195, 200, 370, 687, 853, 880, 899, 961, 963, 1013, 1153, 1161, 1235, 1263, 1291, 1325, 1347, 1357, 1399, 1444, 1451, 1798, 1846, 2067, 2191, 2258, 2305, 2332, 2356, 2370, 2487, 2516, 2571, 2578, 2690, 2694, 2807, 2926, 2956, 3012
Offset: 1
Examples
Moving always to the right in the decimal expansion of e, the string "1" is found at position 2 counting from the first digit after the decimal point, the string "2" is found at position 4, the string "3" at position 17, the string "4" at position 25, etc.
Programs
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Mathematica
p = ToString[FromDigits[RealDigits[N[E - 2, 2600]][[1]]]]; lst = {0}; Do[ a = StringPosition[p, ToString[n], 1][[1, 1]]; AppendTo[lst, a + lst[[-1]]]; p = StringDrop[p, a], {n, 29}]; Rest[lst]