A230980 -id:A230980 - cp's OEIS frontend

A131378 Starting with 0, the sequence a(n) changes from 0 to 1 or back when the next number n is a prime.

0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1

Offset: 0

Paolo P. Lava and Giorgio Balzarotti, Jul 04 2007

Zero together with A071986. - Omar E. Pol, Feb 19 2011

Parity of A230980. - Omar E. Pol, Jul 19 2019

			n = 0, 1, 2, 3, 4, 5, etc.
a(n)= 0, 0, 1, 0, 0, 1, etc.
Starting with 0 the sequence changes when we move from 1 to 2 because 2 is prime, again from 2 to 3 because also 3 is prime, then from 4 to 5 being 5 prime and so on.

Cf. A131377.

Cf. A071986. - Omar E. Pol, Feb 19 2011

P:=proc(n) local i,k; k:=0; for i from 0 by 1 to n do if isprime(i) then if k=1 then k:=0; else k:=1; fi; fi; print(k); od; end: P(100);

nxt[{n_,a_}]:={n+1,Which[a==0&&PrimeQ[n+1],1,a==1&&PrimeQ[n+1],0,True,a]}; NestList[nxt,{0,0},100][[All,2]] (* Harvey P. Dale, Jul 19 2019 *)

A347041 Stirling transform of pi (A000720).

Original entry on oeis.org

0, 0, 1, 5, 21, 88, 389, 1852, 9525, 52632, 310141, 1936489, 12749204, 88149847, 637769490, 4812457992, 37763509549, 307453610201, 2592851608305, 22626572045811, 204197274002794, 1905132039608335, 18370391387293756, 183001650861913887, 1882207129695280320

Offset: 0

Alois P. Heinz, Aug 13 2021

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..575

Cf. A000720, A008277, A048993, A230980, A307771.

b:= proc(n, m) option remember; `if`(n=0,
      numtheory[pi](m), m*b(n-1, m)+b(n-1, m+1))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..27);

G.f.: Sum_{k>=0} pi(k)*x^k / Product_{j=1..k} (1-j*x).
E.g.f.: Sum_{k>=0} pi(k)*(exp(x)-1)^k/k!.
a(n) = Sum_{k=0..n} Stirling2(n,k)*pi(k).

cp's OEIS Frontend

A131378 Starting with 0, the sequence a(n) changes from 0 to 1 or back when the next number n is a prime.

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