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

Author

Paolo P. Lava and Giorgio Balzarotti, May 23 2006

Keywords

• nonn
• easy

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.

Examples

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

Links

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

Crossrefs

Cf. A119487.

Programs

Magma

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

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 *)