# A126148 corrected and prime(i)+prime(i+1)+prime(i)*prime(i+1)

Jonathan Post jvospost3 at gmail.com
Fri Mar 9 03:12:33 CET 2007

```COMMENT FROM Jonathan Vos Post RE A126148

%I A126148
%S A126148 3, 5, 11, 13, 17, 19, 23, 41, 43, 47, 59
%N A126148 Let p and q be consecutive primes. If pq+p+q is a prime,
%C A126148 Correction: since M. Bergot did not specifiy odd primes:
a(n) = 2, 3, 5, 11, 13, 17, 19, 23, 41, 43, 47, 59, ...
A001043 Numbers that are the sum of 2 successive primes.
A006094 Product of 2 successive primes.
The associated sequence prime(i)+prime(i+1)+prime(i)*prime(i+1) =
11, 23, 47, 95, 167, 251, 359, 479, 719, 959, 1215, 1595, 1847... is not
currently in OEIS, nor is the prime subsequence: 11, 23, 47, 167, 251,
359, 479, 719, 1847, 2111...
%F A126148 {p: A001043(n) + A006094(n) is in A000040}.
%e A126148 a(1) = 2 because (2+3)+(2*3) = 5 + 6 = 11 is prime.
a(2) = 3 because (3+5)+(3*5) = 8 + 15 = 23 is prime.
a(3) = 5 because (5+7)+(5*7) = 12 + 35 = 47 is prime.
(7+11)+(7*11) = 18 + 77 = 95 = 5*19 is composite.
a(4) = 11 because (11+13)+(11*13) = 24 + 143 = 167 is prime.
a(5) = 13 because 13+17 + (13*17) = 251 is prime.
a(6) = 17 because 17+19 + (17*19) = 359 is prime.
a(7) = 19 because 19+23 + (19*23) = 479 is prime.
a(8) = 23 because 23+29 + (23*29) = 719 is prime.
29+31 + (29*31) = 959 = 7 * 137 is composite.
31+37 + (31*37) = 1215 = 3^5 * 5 is composite.
37+41 + (37*41) = 1595 = 5 * 11 * 29 is composite.
a(9) = 41 because 41+43 + (41*43) = 1847 is prime.
a(10) = 43 because 43+47 + (43*47) = 2111 is prime.
%Y A126148 Cf. A000040, A001043, A006094.
%O A126148 1
%K A126148 ,easy,nonn,
%A A126148 Jonathan Vos Post (jvospost2 at yahoo.com), Mar 08 2007
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