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

1,2

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

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).

Prog

(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)));

Crossrefs

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

Sequence in context: A292266 A292267 A365392 * A171060 A254596 A373230

Adjacent sequences: A305807 A305808 A305809 * A305811 A305812 A305813

Keyword

nonn

Author

Antti Karttunen, Jun 16 2018

Status

approved