A247824 -id:A247824 - cp's OEIS frontend

A248354 Least positive integer m such that m + n divides prime(m^2) + prime(n^2).

1, 1, 2, 1, 3, 8, 2, 6, 6, 45, 9, 4, 15, 2, 13, 17, 4, 12, 9, 8, 11, 6, 101, 20, 2, 15, 7, 50, 4, 183, 48, 15, 9, 5, 4, 4, 157, 1, 123, 4, 13, 112, 76, 4, 7, 13, 44, 2, 16, 28, 83, 202, 114, 50, 85, 31, 14, 62, 19, 25

Offset: 1

Zhi-Wei Sun, Oct 05 2014

nonn

Conjecture: a(n) exists for any n > 0. Moreover, a(n) <= n*(n-1)/2 for all n > 1.

See also the comments in A248052.

			a(3) = 2 since 2 + 3 = 5 divides prime(2^2) + prime(3^2) = 7 + 23 = 30.

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Cf. A000040, A000290, A011757, A247824, A247975, A248052.

Do[m = 1; Label[aa]; If[Mod[Prime[m^2] + Prime[n^2], m + n] == 0, Print[n, " ", m]; Goto[bb]]; m = m + 1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}]

a(n)=my(N=prime(n^2),m); while((prime(m++^2)+N)%(m+n), ); m \\ Charles R Greathouse IV, Oct 05 2014

A302754 Maximum remainder of prime(p) + prime(q) divided by p + q with p <= q <= n.

Original entry on oeis.org

0, 2, 4, 6, 6, 6, 6, 6, 10, 18, 18, 22, 22, 24, 24, 24, 24, 24, 24, 24, 24, 26, 28, 34, 44, 46, 46, 46, 46, 46, 57, 58, 61, 61, 61, 61, 61, 61, 61, 61, 61, 61, 61, 61, 61, 61, 61, 62, 62, 62, 62, 62, 62, 70, 74, 78, 82, 82, 82, 82, 82, 90, 110, 110, 110, 110, 126, 130, 136, 138, 138, 142, 142, 142, 142

Offset: 1

Andres Cicuttin and Altug Alkan, Apr 12 2018

Odd numbers k which are terms of this sequence are 57, 61, 353, 2113, ...

Approximate self-similar growing patterns appear at different scales which suggest a fractal-like structure, see plots in Links section.

			a(1) = 0 because only option is p = q = 1.
a(4) = a(8) = 6 because (prime(4) + prime(4)) mod 8 = (prime(8) + prime(7)) mod 15 = 6 is the largest remainder for both.
a(31) = 57 because (prime(28) + prime(31)) mod 59 = 57 is the largest remainder.

Altug Alkan, Table of n, a(n) for n = 1..10000
Andres Cicuttin, Several plots showing similar stair-like patterns

Cf. A247824, A302245, A302446.

a[n_]:=Table[Table[Mod[Prime[j]+Prime[i],i+j],{i,1,j}],{j,1,n}]//Flatten//Max;
Table[a[n],{n,1,100}]

a(n) = vecmax(vector(n, q, vecmax(vector(q, p, (prime(p)+prime(q)) % (p+q)))));

cp's OEIS Frontend

A248354 Least positive integer m such that m + n divides prime(m^2) + prime(n^2).

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