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Triprimes modulo 10.
3

%I #23 Aug 17 2024 01:33:25

%S 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,

%T 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,

%U 4,5,6,0,2,0,6,8,2,5,2,3,8,3,5,4,6,7

%N Triprimes modulo 10.

%C Last digit of triprimes (A014612).

%H Reinhard Zumkeller, <a href="/A253721/b253721.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>

%F a(n) = A010879(A014612(n)). - _Michel Marcus_, May 03 2015

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

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

%o (Haskell)

%o a253721 = flip mod 10 . a014612 -- _Reinhard Zumkeller_, May 05 2015

%o (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

%o (Python)

%o from math import isqrt

%o from sympy import primepi, primerange, integer_nthroot

%o def A253721(n):

%o 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)))

%o m, k = n, f(n)

%o while m != k:

%o m, k = k, f(k)

%o return m%10 # _Chai Wah Wu_, Aug 17 2024

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

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

%Y Cf. A255646 (subsequence).

%K nonn,base,easy

%O 1,1

%A _Wesley Ivan Hurt_, May 02 2015