A103271 -id:A103271 - cp's OEIS frontend

A103270 a(n) = (prime(n)+prime(n+k)) mod 4, where k = (prime(n+1)-prime(n))/2.

0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 2

Yasutoshi Kohmoto, Jan 27 2005

nonn

If {prime(n), prime(n+1)} are twin primes, then a(n) = 2*prime(n)+2 = 0 mod 4.

The number of 2's up to n = 2^k, k >= 1, is (0, 0, 0, 1, 4, 9, 30, 72, 162, 346, 779, 1596, 3333, 6867, 13987, 28229,...). Between n = 2^5 and n = 2^16, the percentage of 2's increases from 12.5% to 43%. - M. F. Hasler, Jun 06 2017

M. F. Hasler, Table of n, a(n) for n = 2..10000

Cf. A103271.

See A287868 for positions of 2's.

a:=proc(n) local k: k:=(ithprime(n+1)-ithprime(n))/2: ithprime(n)+ithprime(n+k) mod 4 end: seq(a(n),n=2..130); # Emeric Deutsch, May 31 2005

Table[Mod[Prime[n]+Prime[n+(Prime[n+1]-Prime[n])/2],4],{n,2,120}] (* Harvey P. Dale, Jun 30 2020 *)

a(n)=(prime(n+(prime(n+1)-n=prime(n))/2)+n)%4 \\ M. F. Hasler, May 12 2016

{S=0; L=n=1; o=3; forprime(p=4,,S+=(o+prime((-o+o=p)\2+n++))%4;nM. F. Hasler, Jun 06 2017

More terms from Emeric Deutsch, May 31 2005

A272356 (Sum_{i=1..n} prime(i)) mod 4.

Original entry on oeis.org

0, 2, 1, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 3, 0, 3, 2, 3, 0, 1, 0, 3, 0, 1, 0, 3, 0, 3, 0, 3, 0, 3, 2, 3, 2, 3, 2, 3, 0, 3, 2, 1, 0, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 2, 3, 2, 3, 0, 3, 2, 3, 2, 1, 2, 3, 0, 1, 0, 1, 0, 1, 0, 3, 0, 1, 2, 1, 0, 3, 2, 1, 0, 3, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 3, 0, 3, 0

Offset: 0

M. F. Hasler, Apr 26 2016

nonn

Inspired by A103271, prime(n)+prime(n+1) mod 4.

Cf. A103271, A007504.

A272356(n,print_all=1,a=Mod(0,4))={n&&forprime(p=2,,a+=p;print_all&&print1(lift(a)",");n--||break);lift(a)}

a(n) = A007504(n) mod 4.

cp's OEIS Frontend

A103270 a(n) = (prime(n)+prime(n+k)) mod 4, where k = (prime(n+1)-prime(n))/2.

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A272356 (Sum_{i=1..n} prime(i)) mod 4.

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