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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.
0
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
1,1
FORMULA
a(n) = A045392((n+1)/2) if n is odd, A045458(n/2) if n is even. - Jon E. Schoenfield, Jun 15 2022
EXAMPLE
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.
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
CROSSREFS
Sequence in context: A342386 A374402 A070281 * A198444 A019368 A141171
KEYWORD
nonn
AUTHOR
Zak Seidov, Jun 15 2022
STATUS
approved