A356051 a(n) is the index of the start of the first run of exactly n identical values in A356048.

5, 1, 103, 2683, 2831, 22031, 9105296

Offset

1,1

Comments

a(n) is the least k such that A356048(k) = ... = A356048(k+n-1) but these are different from A356048(k-1) (if k > 1) and A356048(k+n).

a(n) is the index k of the first of exactly n consecutive primes p such that the least primes q for which 2*q^2-p^2 is prime are all equal.

Links

Table of n, a(n) for n=1..7.

Example

a(3) = 103 as A356048(103) = A356048(104) = A356048(105) = 809, while A356048(102) = 811 and A356048(106) = 823 are different.  Thus for prime(103) = 563, prime(104) = 569 and prime(105) = 571 we have 809^2 - 2*563^2 = 20543, 809^2 - 2*569^2 = 6959 and 809^2 - 2*571^2 = 2399 all prime.

Maple

f:= proc(n) local q;
    q:= floor(sqrt(2)*n);
    do
      q:= nextprime(q);
      if isprime(q^2-2*n^2) then return q fi;
    od
end proc;
R:= Vector(6): count:= 0:
p:= 2: v:= f(2): c:= 1:
for k from 2 while count < 6 do
   p:= nextprime(p);
w:= f(p);
   if w = v then c:= c+1
else
    if R[c] = 0 then R[c]:= k-c; count:= count+1 fi;
    v:= w;
    c:= 1;
fi
od:
convert(R, list);

Crossrefs

Cf. A356048.

Sequence in context: A294258 A294260 A113114 * A099740 A362161 A359657

Adjacent sequences: A356048 A356049 A356050 * A356052 A356053 A356054

Keyword

nonn,more

Author

J. M. Bergot and Robert Israel, Jul 24 2022

Status

approved