A253721 Triprimes modulo 10.

8, 2, 8, 0, 7, 8, 0, 2, 4, 5, 0, 2, 3, 6, 8, 0, 5, 6, 8, 2, 8, 9, 2, 5, 0, 4, 6, 7, 4, 5, 0, 8, 7, 8, 3, 4, 4, 5, 0, 1, 2, 4, 5, 2, 6, 8, 0, 5, 7, 2, 2, 0, 1, 6, 8, 2, 4, 5, 6, 5, 8, 1, 6, 8, 3, 5, 9, 2, 4, 5, 6, 0, 2, 0, 6, 8, 2, 5, 2, 3, 8, 3, 5, 4, 6, 7

Offset: 1

Author

Wesley Ivan Hurt, May 02 2015

Keywords

• nonn
• base
• easy

Comments

Last digit of triprimes (A014612).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to final digits of numbers

Crossrefs

Cf. A010879 (final digit of n), A014612 (triprimes).

Cf. A007652 (primes mod 10), A106146 (semiprimes mod 10).

Cf. A255646 (subsequence).

Programs

Haskell

a253721 = flip mod 10 . a014612  -- Reinhard Zumkeller, May 05 2015

Maple

with(numtheory): A253721:=n->`if`(bigomega(n) = 3, n mod 10, NULL): seq(A253721(n), n=1..500);

Mathematica

Mod[#, 10] & /@ Select[Range[500], PrimeOmega[#] == 3 &]

PARI

do(x)=my(v=List(), t); forprime(p=2, x\4, forprime(q=2, min(x\(2*p), p), t=p*q; forprime(r=2, min(x\t, q), listput(v, t*r)))); Set(v)%10 \\ Charles R Greathouse IV, Aug 30 2017

Python

from math import isqrt
from sympy import primepi, primerange, integer_nthroot
def A253721(n):
    def f(x): return int(n+x-sum(primepi(x//(k*m))-b for a,k in enumerate(primerange(integer_nthroot(x,3)[0]+1)) for b,m in enumerate(primerange(k,isqrt(x//k)+1),a)))
    m, k = n, f(n)
    while m != k:
        m, k = k, f(k)
    return m%10 # Chai Wah Wu, Aug 17 2024

Formula

a(n) = A010879(A014612(n)). - Michel Marcus, May 03 2015