A259232 -id:A259232 - cp's OEIS frontend

A259226 Numbers n such that A157480(n) = A259232(n).

2, 3, 7, 12, 14, 19, 29, 36, 37, 38, 42, 46, 50, 67, 73, 74, 82, 84, 106, 110, 112, 125, 134, 143, 157, 168, 169, 177, 183, 202, 222, 226, 232, 249, 263, 275, 278, 282, 314, 327, 355, 369, 399, 433, 457, 464, 483, 557, 617, 685, 820, 826, 835, 838, 935, 937, 1031, 1059, 1080, 1087, 1112, 1205, 1276, 1296, 1316, 1349, 1421, 1503, 1505, 1713, 1827, 2017, 2085, 2092, 2263, 2337, 2357, 2498, 2591, 2594, 2634, 2676, 2771, 2984, 3128, 3776, 3777, 3928, 4382, 5037, 5319, 5448, 5621, 5839, 6137, 6183, 6521, 7373, 9867

Offset: 1

Zak Seidov, Jun 22 2015

Or numbers n such that A157480(n) > A000040(n).

It is a strong conjecture that the sequence is complete, and the last term is a(99)=9867.

Cf. A000040, A157480, A259232.

A259237 a(n) = least prime q such that q + prime(n) is a cube.

Original entry on oeis.org

727, 5, 3, 1721, 53, 499, 47, 197, 41, 971, 1697, 179, 23, 173, 17, 11, 5, 3, 149, 929, 439, 137, 4013, 127, 2647, 1627, 113, 109, 107, 103, 89, 1597, 79, 373, 67, 2593, 59, 53, 3929, 43, 37, 331, 809, 23, 19, 17, 5, 2521, 773, 283, 3863, 761, 271, 5581, 743, 3833

Offset: 1

Zak Seidov, Jun 22 2015

Corresponding values of (a(n)+prime(n))^(1/3): 9,2,2,12,4,8,4,6,4,10,12,6,4,6,4,4,4,4,6,10,8,6,16,6,14,12,6,6,6,6,6.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A157480, A259232.

f:= proc(n) local p,k;
  p:= ithprime(n);
  for k from ceil(p^(1/3)) do
    if isprime(k^3 - p) then return k^3 - p fi
  od
end proc:
map(f, [$1..100]); # Robert Israel, Oct 17 2023

Table[p=Prime[n];x=Ceiling[p^(1/3)];While[!PrimeQ[q=x^3-p],x++];q,{n,100}]

a(n) = {p = prime(n); k=2; while(!ispower(p+k,3), k = nextprime(k+1)); k;} \\ Michel Marcus, Jun 22 2015

A381368 a(n) is the least k > n for which prime(n) + prime(k) is a square.

Original entry on oeis.org

4, 6, 5, 10, 16, 9, 8, 102, 13, 20, 30, 28, 17, 26, 16, 58, 33, 23, 55, 21, 54, 142, 30, 28, 49, 48, 139, 35, 91, 47, 45, 44, 56, 135, 54, 40, 39, 252, 51, 49, 78, 128, 62, 76, 75, 126, 245, 71, 55, 69, 54, 68, 120, 137, 81, 65, 63, 238, 171, 96, 62, 76, 108, 209

Offset: 1

Felix Huber, Mar 02 2025

Least k > n for which A000040(n) + A000040(k) is a term of A000290.

a(1) = 1 if k = n were also permitted. All other terms would remain unchanged.

			a(2) = 6 because prime(2) + prime(6) = 3 + 13 = 4^2 and 3 + 5, 3 + 7, 3 + 11 are not squares.

Felix Huber, Table of n, a(n) for n = 1..10000

Cf. A000040, A000290, A259232.

A381368:=proc(n)
    local k;
        for k from n+1 do
            if issqr(ithprime(n)+ithprime(k)) then
                return k
            fi
        od
end proc;
seq(A381368(n),n=1..64);

a[n_]:=Module[{k=n+1},While[!IntegerQ[Sqrt[Prime[n]+Prime[k]]], k++]; k]; Array[a,64] (* Stefano Spezia, Mar 02 2025 *)

a(n) = my(k=n+1, q=prime(n+1), p=prime(n)); while (!issquare(p+q), k++;q=nextprime(q+1)); k; \\ Michel Marcus, Mar 02 2025

a(n) = A000720(A259232(n)). - Michel Marcus, Mar 02 2025

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A259226 Numbers n such that A157480(n) = A259232(n).

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A259237 a(n) = least prime q such that q + prime(n) is a cube.

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A381368 a(n) is the least k > n for which prime(n) + prime(k) is a square.

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