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A358974
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a(n) is the least prime p such that q-p = n*(r-q) where p,q,r are consecutive primes.
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0
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3, 7, 23, 6397, 139, 509, 84871, 1933, 1259, 43331, 1129, 4523, 933073, 2971, 6917, 1568771, 9973, 32261, 4131109, 25261, 78737, 12809359, 91033, 28229, 13626257, 35677, 117443, 37305713, 399793, 102701, 217795247, 288583, 296843, 240485257, 173359, 1025957, 213158279, 1053103, 370949, 1163010181
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internal format)
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OFFSET
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1,1
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COMMENTS
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a(n) = prime(k) for the first k such that A001223(k) = n*A001223(k+1).
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LINKS
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EXAMPLE
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a(3) = 23 because 23, 29, 31 are consecutive primes with 29-23 = 3*(31-29) and 23 is the first prime that works.
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MAPLE
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V:= Vector(45): count:= 0:
q:= 2: r:= 3:
while count < 45 do
p:= q; q:= r; r:= nextprime(r);
v:= (q-p)/(r-q);
if v::integer and v <= 45 and V[v] = 0 then
count:= count+1; V[v]:= p;
fi
od:
convert(V, list);
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PROG
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(Python)
from sympy import nextprime
from itertools import count, islice
def agen():
p, q, r, n, adict = 2, 3, 5, 1, dict()
while True:
v, rem = divmod(q-p, r-q)
if rem == 0 and v not in adict: adict[v] = p
while n in adict: yield adict[n]; n += 1
p, q, r = q, r, nextprime(r)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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