A338529 -id:A338529 - cp's OEIS frontend

A338533 Primes in A338529/2.

31, 1873, 6163, 4133, 8093, 18211, 10529, 18233, 12743, 14557, 15473, 16057, 16607, 37571, 28793, 22669, 92221, 58073, 65993, 34759, 37781, 32563, 36473, 106163, 70003, 48487, 64621, 75527, 87133, 117701, 89017, 171877, 61223, 61283, 62603, 96997, 75533, 103657, 116797, 81899, 82241, 108533

Offset: 1

J. M. Bergot and Robert Israel, Nov 01 2020

nonn

The primes are listed in the order in which they appear in A338529. Some appear more than once, e.g. a(481) = a(669) = 2427137 because 2427137 = A338529(11966)/2 = A338529(16893)/2.

			A338529(2)/2 = 31 is prime, so a(1) = 31.
A338529(38)/2 = 1873 is prime, so a(2) = 1873.
A338529(65)/2 = 6163 is prime, so a(3) = 6163.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A338529.

select(isprime, [seq(ithprime(n+2)*ithprime(n+3)-ithprime(n)*ithprime(n+1), n=2..10000)]/2);

A338537 Numbers that occur more than once in A338529.

Original entry on oeis.org

4320, 23142, 301310, 333414, 340352, 375650, 553520, 644490, 910872, 921730, 1133670, 1366090, 1422650, 1440138, 1650350, 1705070, 1751970, 1874430, 2091850, 2180768, 2852640, 3213780, 3438548, 3676320, 4044732, 4444662, 4682000, 4854274, 4863754, 5101914, 5384106, 6011250, 6309860, 6551688

Offset: 1

J. M. Bergot and Robert Israel, Nov 01 2020

nonn

Does any number occur more than twice in A338529?

			a(3) = 301310 is in the sequence because A338529(1618) = A338529(2414) = 301310.

Robert Israel, Table of n, a(n) for n = 1..609

Cf. A338529.

A338529:= [seq(ithprime(n+2)*ithprime(n+3)-ithprime(n)*ithprime(n+1), n=1..100000)]):
M:= 12*ithprime(100000):
V:= Vector(M,datatype=integer[4]):
R:= NULL:
for i from 1 to 100000 do
  v:= A338529[i];
  if v <= M then V[v]:= V[v]+1; if V[v] > 1 then R:= R, v fi fi
od:
sort([R]);

A357679 a(n) = prime(n)*(prime(n-1) + prime(n+1)).

Original entry on oeis.org

21, 50, 112, 220, 364, 544, 760, 1104, 1566, 2046, 2664, 3280, 3784, 4512, 5618, 6726, 7686, 8844, 9940, 10950, 12324, 13944, 16020, 18430, 20200, 21424, 22684, 23980, 26668, 30988, 34584, 36990, 39754, 43210, 46206, 49298, 52812, 56112, 59858, 63366, 66970, 71434, 74884, 77224, 81192

Offset: 2

Saish S. Kambali, Oct 09 2022

21 is the only semiprime term.

All terms after 21 are even.

Cf. A000040, A048448, A006094.

Cf. A338529 (first differences).

Array[Prime[# + 1] (Prime[#] + Prime[# + 2]) &, 45] (* Michael De Vlieger, Oct 09 2022 *)

a(n) = prime(n)*(prime(n-1) + prime(n+1)) \\ Michel Marcus, Oct 09 2022

a(n) = A000040(n)*A048448(n).

a(n) = A006094(n) + A006094(n-1).

cp's OEIS Frontend

A338533 Primes in A338529/2.

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A338537 Numbers that occur more than once in A338529.

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A357679 a(n) = prime(n)*(prime(n-1) + prime(n+1)).

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