A119488 Primes of the form prime(i+1)*(i+1) - prime(i)*i, for increasing values of i.

13, 23, 41, 83, 103, 89, 103, 113, 227, 229, 547, 373, 419, 263, 373, 787, 419, 433, 593, 563, 577, 739, 487, 811, 823, 683, 1013, 599, 1153, 641, 827, 1571, 1223, 863, 883, 719, 1567, 1187, 1279, 1999, 1361, 1373, 1951, 1297, 2477, 1091, 1399, 1117, 2897, 1459

Offset

1,1

Comments

Some terms are repeated: e.g. 157*37 - 151*36 = 197*45 - 193*44 = 373.

The first numbers that are repeated 3 times are 96553, 104597, 109793, 139303, etc.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

The fourth prime is 7 and the third is 5.
Therefore 7*4 - 5*3 = 28 - 15 = 13 that is a prime.

Maple

P:=proc(n) local i, j; j:=ithprime(n+1)*(n+1)-ithprime(n)*n;
if isprime(j) then j; fi; end: a:=seq(P(i), i=1..10000);

Mathematica

Select[#[[2]] - #[[1]] &/@ Partition[Table[n Prime[n], {n, 300}], 2, 1], PrimeQ] (* Harvey P. Dale, Jun 05 2017 *)

Prog

(Magma) [m: i in [1..300] | IsPrime(m) where m is NthPrime(i+1)*(i+1)-NthPrime(i)*i]; // Bruno Berselli, Jun 06 2017

Crossrefs

Cf. A119487.

Sequence in context: A135283 A225519 A213655 * A165350 A236418 A112394

Adjacent sequences: A119485 A119486 A119487 * A119489 A119490 A119491

Keyword

nonn,easy

Author

Paolo P. Lava and Giorgio Balzarotti, May 23 2006

Status

approved