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Self-locating strings within e: numbers k such that the string k is at position k (after the decimal point) in the decimal digits of e, where 7 is the 0th digit.
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%I #24 Dec 19 2022 13:55:52

%S 1,8,215,374,614,849,4142,7945,5964055,8008913,7131377227,8829981707

%N Self-locating strings within e: numbers k such that the string k is at position k (after the decimal point) in the decimal digits of e, where 7 is the 0th digit.

%e The first two terms 1 and 8 are depicted here:

%e Position: 0123456789...

%e Digits of e: 2.7182818284...

%e .^......^....

%e 1 is the first term because 1 is in position 1 after the decimal point (when starting to count with 0).

%e 8 is the second term because 8 is in position 8 etc.

%o (Python)

%o # after _Michael S. Branicky_ in A064810

%o # First get a file with e digits, e.g. https://www4.baumann.at/downloads/e.txt

%o with open('e.txt', 'r') as f: digits_of_e = f.readline()[2:]

%o def afind():

%o global digits_of_e

%o for k in range(len(digits_of_e)):

%o s = str(k)

%o if digits_of_e[k:k+len(s)] == s: print(k, end=", ")

%o afind()

%Y Cf. A001113, A064810, A205648.

%K base,nonn,more

%O 0,2

%A _Chris Baumann_, Nov 04 2022

%E a(9)-a(12) from _Michael S. Branicky_, Nov 04 2022