A157187 -id:A157187 - 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}

A218862 The least number having n representations as p*q - p - q for primes p <= q.

Original entry on oeis.org

2, 0, 3, 35, 71, 1151, 1079, 4199, 11879, 7559, 32759, 30239, 75599, 171359, 241919, 251999, 262079, 393119, 604799, 665279, 1572479, 1834559, 2827439, 2570399, 2358719, 7862399, 7814015, 5405399, 6683039, 18017999, 20180159, 8648639, 17992799, 17297279

Offset: 0

T. D. Noe, Dec 06 2012

nonn

a(72) > 2^32. - Donovan Johnson, Dec 07 2012

			The values of a(n) and (p,q) for n = 1 to 6:
0 is    (2,2).
3 is    (2,5),    (3,3).
35 is   (2,37),   (3,19),  (7,7).
71 is   (2,73),   (3,37),  (5,19),  (7,13).
1151 is (2,1153), (3,577), (7,193), (13,97),  (17,73).
1079 is (3,541),  (5,271), (7,181), (11,109), (19,61), (31,37).

Donovan Johnson, Table of n, a(n) for n = 0..71

Cf. A157187.

nn = 10000; ps = Prime[Range[PrimePi[nn + 1]]]; t = Table[0, {nn}]; Do[n = p*q - p - q; If[p <= q && 0 < n <= nn, t[[n]]++], {p, ps}, {q, ps}]; t = Join[{1}, t]; u = Union[t]; c = Complement[Range[Max[u]], u]; If[c == {}, mx = u[[-1]], mx = c[[-1]] - 1]; Table[Position[t, n, 1, 1][[1, 1]] - 1, {n, 0, mx}]

A157189 Records in A157188.

Original entry on oeis.org

0, 2, 3, 4, 5, 6, 9, 10, 11, 12, 14, 16, 17, 19, 20, 22, 23, 25, 26, 27, 31, 32, 33, 34, 37, 42, 45, 46, 54, 58, 61, 65, 70, 71, 73, 76, 77, 78, 87, 100

Offset: 1

M. F. Hasler, Mar 11 2009

nonn

The corresponding primes are given in A157190.

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

Cf. A157187-A157190

a(n) = A157187(A157190(n)) > A157187(p) for all primes p < A157190(n).

Corrected a(29), deleted spurious term 52 M. F. Hasler, Mar 15 2009

cp's OEIS Frontend

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

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

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A218862 The least number having n representations as p*q - p - q for primes p <= q.

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Mathematica

A157189 Records in A157188.

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