A355025 a(1)=2; for n > 1, a(n) is the least new prime such that a(n-1) + a(n) is a multiple of 7.

2, 5, 23, 19, 37, 47, 79, 61, 107, 89, 149, 103, 163, 131, 191, 173, 233, 229, 317, 257, 331, 271, 359, 313, 373, 383, 401, 397, 443, 439, 457, 467, 499, 509, 541, 523, 569, 593, 653, 607, 709, 677, 751, 691, 821, 719, 863, 733, 877, 761

Offset: 1

Author

Zak Seidov, Jun 15 2022

Keywords

• nonn

Examples

			2 + 3 = 5 is not a multiple of 7, but 2 + 5 = 7 is, so a(2) = 5.
5 + 2 = 7 is a multiple of 7, but 2 is already a term; 5 + 3 = 8, 5 + 7 = 12, ..., 5 + 19 = 24 are not multiples of 7, but 5 + 23 = 28 is, so a(3) = 23.
23 + 5 = 28 is a multiple of 7, but 5 is already a term; 19 is the next prime p such that 7 divides 23 + p, so a(4) = 19.
		

Crossrefs

Cf. A045392, A045458.

Programs

Mathematica

s = {2}; Do[p = 3; a = s[[-1]]; While[MemberQ[s, p] || Mod[a + p, 7] != 0, p = NextPrime[p]]; AppendTo[s, p], {100}]; s

Formula

a(n) = A045392((n+1)/2) if n is odd, A045458(n/2) if n is even. - Jon E. Schoenfield, Jun 15 2022