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

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

Author

Andres Cicuttin and Altug Alkan, Apr 12 2018

Keywords

• nonn
• look

Comments

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A247824, A302245, A302446.

Programs

Mathematica

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}]

PARI

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