A305810 Filter sequence for a(Sophie Germain primes > 3) = constant sequences.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 5, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 5, 22, 23, 24, 25, 26, 5, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 5, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 5, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 5, 78, 79, 80, 81, 82, 5, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 5

Offset: 1

Author

Antti Karttunen, Jun 16 2018

Keywords

• nonn

Comments

Filer sequence for all such sequences S, for which S(A005384(k)) = constant for all k >= 3.

Restricted growth sequence transform of the ordered pair [A305900(n), A305901(1+n)].

For all i, j:

a(i) = a(j) => A305900(i) = A305900(j),

a(i) = a(j) => A305901(1+i) = A305901(1+j),

a(i) = a(j) => A305978(i) = A305978(j),

a(i) = a(j) => A305985(i) = A305985(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A005384, A156660, A156874, A305900, A305901, A305978, A305985.

Programs

PARI

up_to = 100000;
A156660(n) = (isprime(n)&&isprime(2*n+1)); \\ From A156660
partialsums(f,up_to) = { my(v = vector(up_to), s=0); for(i=1,up_to,s += f(i); v[i] = s); (v); }
v156874 = partialsums(A156660, up_to);
A156874(n) = v156874[n];
A305810(n) = if(n<5,n,if(A156660(n),5,3+n-A156874(n)));

Formula

If n < 5, a(n) = n; for n >= 5, a(n) = 5 if A156660(n) == 1 [when n is in A005384[3..] = 5, 11, 23, 29, 41, 53, 83, 89, 113, ...], otherwise a(n) = 3+n-A156874(n).