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A259142 Least prime p of the form n*q^2+(n+1)*r^2 with q and r prime. 1
17, 83, 43, 61, 149, 199, 263, 113, 331, 139, 383, 373, 173, 191, 199, 569, 587, 547, 251, 269, 277, 757, 1223, 1321, 859, 347, 787, 373, 3779, 1789, 1063, 953, 433, 1181, 1019, 1069, 1283, 503, 2311, 5209, 1193, 1453, 563, 1301, 2389, 607, 1367, 1657, 641, 659, 1483, 1777, 1811, 1861, 719, 1913, 1657, 1997, 4391, 3229, 797, 1823 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Values of {p,q,r}: {17,3,2},{83,2,5},{43,3,2},{61,2,3},{149,5,2},{199,2,5},{263,3,5},{113,2,3}.

a(2) = A084866(1). - Michel Marcus, Jun 20 2015

For p in A093191, a((p-4)/13) = p. - Robert Israel, Apr 30 2018

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Zak Seidov, First 100 values of {p,q,r}.

EXAMPLE

17=1*3^2+2*2^2, 83=2*2^2+3*5^2, 43=3*3^2+4*2^2.

MAPLE

P:= [seq(ithprime(i), i=1..20)]: np:= 20:

for n from 1 to 100 do

  found:= false;

  while not found do

    R:= sort([seq(seq(n*q^2+(n+1)*p^2, p=P), q=P)]);

    w:= n*4+(n+1)*P[-1]^2+1;

    r:= ListTools:-SelectFirst(isprime, R);

    if r <> NULL and r <= w then

      A[n]:= r;

      found:= true;

    else

      P:= [op(P), seq(ithprime(i), i=np+1..np+20)];

      np:= np+20;

    fi

  od;

od:

seq(A[i], i=1..100); # Robert Israel, Apr 30 2018

CROSSREFS

Cf. A000040, A093191.

Sequence in context: A053820 A294288 A296401 * A142059 A318743 A193046

Adjacent sequences:  A259139 A259140 A259141 * A259143 A259144 A259145

KEYWORD

nonn,look

AUTHOR

Zak Seidov, Jun 19 2015

STATUS

approved

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Last modified July 24 02:56 EDT 2019. Contains 325290 sequences. (Running on oeis4.)