Tjandra Satria Gunawan - cp's OEIS frontend

User: Tjandra Satria Gunawan

Tjandra Satria Gunawan has authored 2 sequences.

A214506 Last digit of the smallest prime number in base 10 with n digits.

2, 1, 1, 9, 7, 3, 3, 9, 7, 7, 9, 3, 9, 7, 1, 7, 1, 3, 3, 1, 9, 7, 9, 7, 7, 3, 7, 3, 1, 9, 7, 3, 9, 1, 3, 9, 7, 3, 3, 3, 1, 9, 3, 7, 1, 9, 1, 3, 3, 9, 1, 1, 7, 1, 1, 1, 3, 9, 9, 9, 7, 3, 7, 1, 7, 9, 9, 9, 9, 9, 3, 3, 9, 9, 7, 9, 3, 1, 3, 9, 9, 3, 1, 7, 1, 3

Offset: 1

Tjandra Satria Gunawan, Jul 19 2012

The last digit of the first prime number in base 10 with n digits for n = 1, 2, 3 is 211, because 2 is the least with 1 digit, 11 the least with 2 digits, 101 the least with 3 digits. The concatenation, 211, is prime. This does not happen again through 24 digits. - Jonathan Vos Post, Jul 04 2012

Table[Mod[NextPrime[10^n],10],{n,0,30}] (* Harvey P. Dale, Jan 25 2013 *)

a(1) = 2, and a(n) = A033873(n) mod 10 for n>1.

a(n) = A003617(n) mod 10. - Michel Marcus, Aug 06 2013

More terms from Harvey P. Dale, Jan 25 2013

A214344 Number of 1's in the first 10^n binary digits in the stream of prime numbers in base 2.

Original entry on oeis.org

1, 8, 69, 593, 5723, 56090, 541794, 5369528, 53803123, 527428642, 5249946808, 52800311682

Offset: 0

Tjandra Satria Gunawan, Jul 13 2012

Consider the stream (concatenation) of binary digits of primes in the MSB-first order featured in A191232. a(n) is the total count of 1's in the first 10^n of zeros and ones in this stream.

The complementary count of 0's is 10^n - a(n) = 0, 2, 31, 407, 4277, 43910, 458206, ... - R. J. Mathar, Jul 16 2012

Cf. A095375.

A214344 := proc()
    local stre,len,ct,p ;
    stre := [] ;
    len := 2 ;
    ct := 1 ;
    p := 2 ;
    while true do
        if nops(stre) = 0 then
            p := nextprime(p) ;
            stre := convert(p,base,2) ;
        end if;
        if op(-1,stre) = 1 then
            ct := ct+ 1;
        end if;
        stre := subsop(-1=NULL,stre) ;
        len := len+1 ;
        if ilog10(len-1) <> ilog10(len) then
            print(ct) ;
        end if;
    end do:
end proc: # R. J. Mathar, Jul 14 2012

pow = 1; sum1 = 0; sum2 = 0; p = 2;seq={}; k = 0; Do[d = IntegerDigits[p, 2]; sum1 += Count[d, 1]; sum2 += Length[d]; k++; If[sum2 >= pow, del = sum2 - pow; term = sum1 - Count[d[[-del ;; -1]], 1];   AppendTo[seq, term]; pow *= 10]; p = NextPrime[p], {10^4}]; seq (* Amiram Eldar, May 10 2019 *)

from sympy import nextprime
from itertools import islice
def bgen(p=2):
    while True: yield from (int(b) for b in bin(p)[2:]); p = nextprime(p)
def a(n): return sum(islice(bgen(), 10**n))
print([a(n) for n in range(7)]) # Michael S. Branicky, Jul 03 2022

a(9)-a(11) from Amiram Eldar, May 10 2019

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User: Tjandra Satria Gunawan

A214506 Last digit of the smallest prime number in base 10 with n digits.

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