A106146 -id:A106146 - cp's OEIS frontend

A239634 Initial digits of semiprimes in decimal representation.

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

Offset: 1

Reinhard Zumkeller, Mar 23 2014

a(n) = A000030(A001358(n)).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A239639 (run lengths), A106146 (last digits).

Haskell
```
a239634 = a000030 . a001358
```

First[IntegerDigits[#]]&/@Select[Range[300],PrimeOmega[#]==2&] (* Harvey P. Dale, Jul 24 2017 *)

A253721 Triprimes modulo 10.

Original entry on oeis.org

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

Wesley Ivan Hurt, May 02 2015

Last digit of triprimes (A014612).

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

Cf. A010879 (final digit of n), A014612 (triprimes).
Cf. A007652 (primes mod 10), A106146 (semiprimes mod 10).
Cf. A255646 (subsequence).

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

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

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

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

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

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

A176146 a(n) = n-th-semiprime without last digit.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 19, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 22, 22, 23, 23, 24, 24, 25

Offset: 1

Giovanni Teofilatto, Apr 10 2010

Sequence A131109 shows that a(n+1)-a(n) can be larger than 1. [From T. D. Noe, Apr 12 2010]

The differences exceed 1 for the first time between a(186) = 59 and a(187) = 61. [R. J. Mathar, Apr 12 2010]

Cf. A176044, A001358, A106146.

cp's OEIS Frontend

A239634 Initial digits of semiprimes in decimal representation.

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A253721 Triprimes modulo 10.

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A176146 a(n) = n-th-semiprime without last digit.

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