A157189 -id:A157189 - cp's OEIS frontend

A157190 Primes which produce records in A157188, at index i=pi(a(n)) (pi=A000720).

2, 3, 59, 71, 1151, 2399, 7559, 42839, 110879, 181439, 241919, 262079, 453599, 665279, 1713599, 2827439, 6425999, 11309759, 12700799, 14137199, 16707599, 37837799, 45239039, 64864799, 82162079, 86486399, 93562559, 260124479, 410810399, 735134399, 950019839

Offset: 1

M. F. Hasler, Mar 11 2009

nonn

Primes that can be written in more ways as p*q-(p+q) (p,q prime) than any smaller prime.

M. F. Hasler, Table of n, a(n), for n=1..40.
Carlos Rivera, Puzzle 482: Two Bergot questions, The Prime Puzzles & Problems Connection.

Cf. A000720, A157187, A157188, A157189, A336296.

A157187(a(n)) = A157188(A000720(a(n))) > A157187(p) for all primes p < a(n).

a(28) corrected by M. F. Hasler, Mar 15 2009

A157188 Number of ways to write prime(n) as p*q-(p+q) with primes p<=q.

Original entry on oeis.org

0, 2, 1, 1, 2, 0, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 3, 0, 0, 4, 0, 1, 1, 0, 0, 1, 1, 2, 0, 0, 0, 2, 1, 1, 1, 0, 0, 1, 2, 0, 3, 0, 3, 0, 1, 1, 1, 1, 1, 0, 0, 3, 0, 2, 0, 2, 1, 1, 0, 1, 0, 0, 0, 4, 0, 0, 1, 0, 2, 0, 0, 4, 0, 0, 1, 2, 0, 0, 0, 0, 4, 0, 4, 0, 0, 1, 0, 0, 1, 1, 1, 3, 0, 1, 1, 3, 0, 1, 1, 0, 0, 0, 1, 1, 0

Offset: 1

M. F. Hasler, Mar 11 2009

nonn

Records in this sequence are given in A157189, the corresponding primes in A157190.

			a(1)=0 since prime(1) = 2 cannot be written as pq-(p+q) for primes p,q.
a(2)=2 since prime(2) = 3 = 2*5-(2+5) = 3*3-(3+3) are the two possibilities.

C. Rivera (Ed.), Puzzle 482: Two Bergot questions, March 2009.

Cf. A157187-A157190

A157188(n)={ local(c=0,L=sqrtint(n=prime(n)+1)); fordiv( n,d, d>L&break; isprime(d+1) || next; isprime(n/d+1) & c++);c}

cp's OEIS Frontend

A157190 Primes which produce records in A157188, at index i=pi(a(n)) (pi=A000720).

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