A031216 -id:A031216 - cp's OEIS frontend

A375525 a(n) = numerator of Sum_{i=1..n} 1/A031216(i).

1, 5, 31, 247, 529, 559, 1747, 181, 4651, 147331, 1276726, 10379813, 10527373, 501426731, 507546131, 14874882499, 120130384067, 8121140473289, 597694372183697, 7829048769596861, 7886595152525441, 341425446875737163, 26430832817384951, 2579018441538210647, 137426518826740878691

Offset: 1

N. J. A. Sloane, Aug 30 2024

			The first few fractions are 1/2, 5/6, 31/30, 247/210, 529/420, 559/420, 1747/1260, 181/126, 4651/3150, 147331/97650, 1276726/830025, 10379813/6640200, 10527373/6640200, ...

Alois P. Heinz, Table of n, a(n) for n = 1..882

Cf. A031216, A375526.

b:= n-> (l-> add(l[i]*11^(i-1), i=1..nops(l)))(convert(ithprime(n),base,10)):
g:= proc(n) option remember; `if`(n<1, 0, g(n-1)+1/b(n)) end:
a:= n-> numer(g(n)):
seq(a(n), n=1..25);  # Alois P. Heinz, Aug 30 2024

a(n) = numerator(sum(i=1, n, 1/fromdigits(digits(prime(i)), 11))); \\ Michel Marcus, Aug 31 2024

A375526 a(n) = denominator of Sum_{i=1..n} 1/A031216(i).

Original entry on oeis.org

2, 6, 30, 210, 420, 420, 1260, 126, 3150, 97650, 830025, 6640200, 6640200, 312089400, 312089400, 9050592600, 72404740800, 4851117633600, 354131587252800, 4603710634286400, 4603710634286400, 197959557274315200, 15227658251870400, 1477082850431428800, 78285391072865726400

Offset: 1

N. J. A. Sloane, Aug 30 2024

			The first few fractions are 1/2, 5/6, 31/30, 247/210, 529/420, 559/420, 1747/1260, 181/126, 4651/3150, 147331/97650, 1276726/830025, 10379813/6640200, 10527373/6640200, ...

Alois P. Heinz, Table of n, a(n) for n = 1..882

Cf. A031216, A375525.

b:= n-> (l-> add(l[i]*11^(i-1), i=1..nops(l)))(convert(ithprime(n),base,10)):
g:= proc(n) option remember; `if`(n<1, 0, g(n-1)+1/b(n)) end:
a:= n-> denom(g(n)):
seq(a(n), n=1..25);  # Alois P. Heinz, Aug 30 2024

a(n) = denominator(sum(i=1, n, 1/fromdigits(digits(prime(i)), 11))); \\ Michel Marcus, Aug 31 2024

cp's OEIS Frontend

A375525 a(n) = numerator of Sum_{i=1..n} 1/A031216(i).

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