cp's OEIS Frontend

A231336 Integers n such that appending some decimal digit to the first n digits of Pi results in a prime.

%I A231336 #15 Aug 14 2022 13:24:17
%S A231336 0,1,2,5,11,12,18,37,39,77,82,100,125,128,220,305,601,676,1692,1901,
%T A231336 2202,2253,2394,3318,3970,5826,7001,9853,12607,13434,16207
%N A231336 Integers n such that appending some decimal digit to the first n digits of Pi results in a prime.
%C A231336 A140515 is a proper subsequence. A060421 - 1 is a proper subsequence. So the terms 47576 & 78072 are also members.
%e A231336 0 is in the sequence since 2, 3, 5, and 7 are all primes;
%e A231336 1 is in the sequence since 31 and 37 are both primes;
%e A231336 2 is in the sequence since 311, 313, and 317 are all primes;
%e A231336 3 is not in the sequence since 3141, 3143, 3147, and 3149 are all composites;
%e A231336 4 is not in the sequence since 31411, 31413, 31417, and 31419 are all composites;
%e A231336 5 is in the sequence since 314159 is a prime; etc.
%t A231336 fQ[n_] := Union[PrimeQ[ 10 IntegerPart[10^n*Pi] + {1, 3, 7, 9}]][[-1]]; k = -1; lst = {}; While[k < 17001, If[ fQ@ k, AppendTo[lst, k + 1]; Print[k + 1]]; k++]; lst
%t A231336 Module[{nn=16300,pd},pd=RealDigits[Pi,10,nn][[1]];Select[Range[0,nn],AnyTrue[ 10*FromDigits[Take[pd,#]]+{1,3,7,9},PrimeQ]&]] (* _Harvey P. Dale_, Aug 14 2022 *)
%o A231336 (PARI) is(n)=my(d=Pi*10^n\10*10);isprime(d+1) || isprime(d+3) || isprime(d+7) || isprime(d+9) \\ _Charles R Greathouse IV_, Nov 07 2013
%Y A231336 Cf. A140515, A060421, A005042.
%K A231336 nonn,base
%O A231336 1,3
%A A231336 _Marvin Ray Burns_ and _Robert G. Wilson v_, Nov 07 2013
%E A231336 Keyword "base" added by _Zak Seidov_, Nov 11 2013