A231336 Integers n such that appending some decimal digit to the first n digits of Pi results in a prime.
0, 1, 2, 5, 11, 12, 18, 37, 39, 77, 82, 100, 125, 128, 220, 305, 601, 676, 1692, 1901, 2202, 2253, 2394, 3318, 3970, 5826, 7001, 9853, 12607, 13434, 16207
Offset: 1
Examples
0 is in the sequence since 2, 3, 5, and 7 are all primes; 1 is in the sequence since 31 and 37 are both primes; 2 is in the sequence since 311, 313, and 317 are all primes; 3 is not in the sequence since 3141, 3143, 3147, and 3149 are all composites; 4 is not in the sequence since 31411, 31413, 31417, and 31419 are all composites; 5 is in the sequence since 314159 is a prime; etc.
Programs
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Mathematica
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 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 *) -
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
Extensions
Keyword "base" added by Zak Seidov, Nov 11 2013
Comments