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Numbers k such that the reverse of the first k digits in the decimal expansion of Pi forms a prime.
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%I #46 Feb 07 2025 00:33:28

%S 1,2,5,6,7,11,15,712,7599,13280,13281,21598,23233

%N Numbers k such that the reverse of the first k digits in the decimal expansion of Pi forms a prime.

%C The initial digits of a few corresponding primes are in A007523. The last one a(10)=768556......62951413 is a prime with 13280-digit. That is A092845(13279).

%C a(14) > 50000. - _Michael S. Branicky_, Feb 06 2025

%e 1 is a term as the first digit of pi, 3, reversed is prime. 2 is a term as the first two digits of pi, 31, reversed is prime. 3 is not a term as the first three digits of pi, 314, reversed, is not prime. - _David A. Corneth_, Feb 13 2017

%t Do[If[PrimeQ[FromDigits[Reverse[IntegerDigits[Floor[Pi*10^(n - 1)]]]]],Print[n]],{n, 13335}]

%t Module[{pid=RealDigits[Pi,10,20000][[1]]},Select[Range[16000],PrimeQ[ FromDigits[ Reverse[Take[pid,#]]]]&]] (* _Harvey P. Dale_, Sep 06 2019 *)

%Y Cf. A092845, A007523, A011545.

%K nonn,more,base,less,changed

%O 1,2

%A _XU Pingya_, Feb 13 2017

%E a(11)-a(13) from _Michael S. Branicky_, Feb 06 2025