A129517 -id:A129517 - cp's OEIS frontend

A129518 Numbers k > 2 such that k divides (k-2)!! - 1 and (k-3)!! - 1.

3, 7, 47, 59, 79, 83, 103, 107, 127, 139, 191, 199, 211, 251, 263, 283, 307, 331, 367, 379, 383, 431, 467, 479, 499, 503, 547, 587, 599, 607, 631, 643, 659, 727, 743, 811, 823, 827, 839, 859, 863, 883, 887, 907, 971, 991, 1087, 1151, 1163, 1171, 1259, 1283

Offset: 1

Alexander Adamchuk, Apr 18 2007

nonn

All terms are primes of the form 4m+3 belonging to A002145. A002145 is the union of this sequence and A129517 (odd primes p such that p divides (p-1)!! - 1).

Odd numbers k > 1 such that k divides (k-1)!! + 1. - Thomas Ordowski, Jul 26 2016

Cf. A006882 (double factorials).
Cf. A002145 (primes of form 4k+3).
Cf. A129517 (odd primes p such that p divides (p-1)!! - 1).
Cf. A129516 (numbers k such that k divides (k-1)!! - 1).
Cf. A260298.

Select[Range[3,2000],IntegerQ[((#-2)!!-1)/# ]&&IntegerQ[((#-3)!!-1)/# ]&]

A129516 Numbers k such that k divides (k-1)!! - 1.

Original entry on oeis.org

1, 2, 8, 11, 16, 19, 23, 31, 32, 43, 64, 67, 71, 128, 131, 151, 163, 167, 179, 223, 227, 239, 256, 271, 311, 347, 359, 419, 439, 443, 463, 487, 491, 512, 523, 563, 571, 619, 647, 683, 691, 719, 739, 751, 787, 911, 919, 947, 967, 983, 1019, 1024, 1031, 1039

Offset: 1

Alexander Adamchuk, Apr 18 2007

nonn

Terms include all powers of 2 except 2^2 and some primes of the form 4m+3 belonging to A002145. Odd primes in this sequence are listed in A129517. A002145 is the union of A129517 and A129518 (numbers m > 2 such that m divides (m-2)!!-1 and (m-3)!!-1).

Cf. A006882 (double factorials).
Cf. A002145 (primes of the form 4k+3).
Cf. A129517 (odd primes p such that p divides (p-1)!!-1).
Cf. A129518 (numbers k > 2 such that k divides (k-2)!!-1 and (k-3)!!-1).

Select[Range[2048],IntegerQ[((#-1)!!-1)/# ]&]

A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2pq, ar=a*b/2; s=a+b+c, s-+1 are primes.

Original entry on oeis.org

2, 3, 11, 71, 227, 491, 683, 1103, 1187, 2591, 3923, 4271, 4931, 6737, 7193, 7703, 8093, 8753, 8963, 9173, 9377, 10271, 13043, 13451, 13997, 15233, 15443, 15803, 15887, 17957, 18701, 19961, 20681, 21701, 22031, 22073, 24371, 24473, 24683

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

nonn

p=1, q=2(prime), a=3, b=4, c=5, s=12-+1 primes, ...

Cf. A020882, A020886, A020884, A020883, A024364, A024406, A155171, A155173, A155174, A155175, A155176, A155177, A155178, A155180, A088483, A001844, A096891, A066885, A099776, A110494, A081589, A155185, A019389, A062090, A050150, A155186, A068231, A129517, A054574, A132281.

lst={};Do[p=n;q=p+1;a=q^2-p^2;c=q^2+p^2;b=2*p*q;ar=a*b/2;s=a+b+c;If[PrimeQ[s-1]&&PrimeQ[s+1],If[PrimeQ[q],AppendTo[lst,q]]],{n,8!}];lst

cp's OEIS Frontend

A129518 Numbers k > 2 such that k divides (k-2)!! - 1 and (k-3)!! - 1.

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A129516 Numbers k such that k divides (k-1)!! - 1.

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A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2pq, ar=a*b/2; s=a+b+c, s-+1 are primes.

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cp's OEIS Frontend

A129518 Numbers k > 2 such that k divides (k-2)!! - 1 and (k-3)!! - 1.

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A129516 Numbers k such that k divides (k-1)!! - 1.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2*p*q, ar=a*b/2; s=a+b+c, s-+1 are primes.

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A155187 Prime numbers q of primitive Pythagorean triangles such that perimeters are averages of twin prime pairs, p+1=q(prime), a=q^2-p^2, c=q^2+p^2, b=2pq, ar=a*b/2; s=a+b+c, s-+1 are primes.