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A351693 a(n) is the least prime prime(k) for which A351692(k) = n, or 0 if there is no such prime. 2
2, 3, 29, 13, 47, 19, 31, 647, 101, 107, 181, 569, 109, 839, 199, 811, 283, 373, 97, 73, 151, 79, 229, 149, 103, 443, 401, 701, 167, 751, 1901, 347, 379, 197, 157, 227, 673, 193, 383, 277, 353, 991, 313, 359, 419, 337, 911, 461, 1319, 1279, 349, 757, 2957, 1747, 827, 631, 457, 1511, 1249, 1559, 1091 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) = prime(k) for the least k such that prime(k)+2*prime(k+j) and prime(k)+2*prime(k-j) are both prime for j = n but not both prime for j = 1 ... n-1.

LINKS

Robert Israel, Table of n, a(n) for n = 0..1000

EXAMPLE

a(3) = 13 = prime(6) because A351692(6) = 3 and A351692(k) <> 3 for 1 <= k < 6.

MAPLE

nP:= 10000: Primes:= [seq(ithprime(i), i=1..nP)]: R:= 2: found:= true:

for n from 1 to 300 while found do

found:= false;

  for k from n+1 to nP-n do

    if isprime(Primes[k]+2*Primes[k-n]) and isprime(Primes[k]+2*Primes[k+n]) and

      andmap(t -> not isprime(Primes[k]+2*Primes[k-t]) or not

        isprime(Primes[k]+2*Primes[k+t]), [$1..n-1]) then

        R:= R, Primes[k]; found:= true; break

    fi

od od:

R;

PROG

(PARI) f(n) = for (k=1, n-1, my(p=prime(n)); if (isprime(p + 2*prime(n-k)) && isprime(p + 2*prime(n+k)), return(k))); return(0); \\ A351692

a(n) = my(k=1); while (f(k) != n, k++); prime(k); \\ Michel Marcus, May 11 2022

CROSSREFS

Cf. A000040, A351692.

Sequence in context: A206591 A003017 A096580 * A324941 A028868 A081332

Adjacent sequences:  A351690 A351691 A351692 * A351694 A351695 A351696

KEYWORD

nonn

AUTHOR

J. M. Bergot and Robert Israel, May 05 2022

STATUS

approved

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Last modified September 30 11:00 EDT 2022. Contains 357105 sequences. (Running on oeis4.)