A037165 a(n) = prime(n)*prime(n+1) - prime(n) - prime(n+1).

1, 7, 23, 59, 119, 191, 287, 395, 615, 839, 1079, 1439, 1679, 1931, 2391, 3015, 3479, 3959, 4619, 5039, 5615, 6395, 7215, 8447, 9599, 10199, 10811, 11447, 12095, 14111, 16379, 17679, 18767, 20423, 22199, 23399, 25271, 26891, 28551, 30615, 32039

Offset: 1

Author

Armand Turpel (armandt(AT)unforgettable.com)

Keywords

• nonn
• easy

Comments

a(n) is also the Frobenius number of the numerical semigroup generated by prime(n) and prime(n+1). - Victoria A Sapko (vsapko(AT)math.unl.edu), Feb 21 2001

Links

• Joshua Oliver, Table of n, a(n) for n = 1..2000 (first 1000 terms from Vincenzo Librandi)
• R. Fröberg, C. Gottlieb and R. Häggkvist, On numerical semigroups, Semigroup Forum, 35 (1987), 63-83 (for definition of Frobenius number).

Crossrefs

Frobenius numbers for k successive primes: this sequence (k=2), A138989 (k=3), A138990 (k=4), A138991 (k=5), A138992 (k=6), A138993 (k=7), A138994 (k=8).

Cf. A001043, A006094.

Programs

Magma

[NthPrime(n)*NthPrime(n+1)-NthPrime(n)-NthPrime(n+1): n in [1..45]]; // Vincenzo Librandi, Dec 18 2012

Mathematica

f[n_] := FrobeniusNumber[{Prime[n], Prime[n + 1]}]; Array[f, 41] (* Robert G. Wilson v, Aug 04 2012 *)
Times@@#-Total[#]&/@Partition[Prime[Range[50]],2,1] (* Harvey P. Dale, Dec 27 2015 *)

PARI

a(n)=my(p=prime(n),q=nextprime(p+1)); p*q-p-q \\ Charles R Greathouse IV, Apr 28 2015

Formula

a(n) = A006094(n) - A001043(n). - Michel Marcus, Mar 02 2019