A340060 Averages k of twin primes such that the sum (with multiplicity) of prime factors of k-1, k and k+1 is prime.

6, 12, 108, 420, 432, 462, 1020, 1290, 1302, 1428, 1482, 2088, 3120, 3468, 3540, 4092, 4242, 5280, 5652, 5850, 5868, 6690, 7332, 8820, 9420, 9462, 9930, 10038, 10092, 11118, 11832, 11940, 14628, 16140, 16362, 17208, 17388, 17682, 18042, 18312, 20640, 20772, 22278, 22962, 23028, 23202, 25848

Offset

1,1

Links

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

Example

a(3)=108 is a term because 107 and 109 are primes and the sum of prime factors of 107, 108=2^2*3^3 and 109 is 107+2+2+3+3+3+109 = 229, which is prime.

Maple

P:= select(isprime, {seq(i, i=3..10^6, 2)}):
T:= map(`+`, P, 1) intersect map(`-`, P, 1):
filter:= proc(t) local s; isprime(2*t+add(s[1]*s[2], s=ifactors(t)[2])) end proc:
sort(convert(select(filter, T), list));

Crossrefs

Subset of A014574. Cf. A001414, A046363.

a(n) = A330488(n)+1.

Sequence in context: A003613 A099767 A191462 * A080450 A144760 A207838

Adjacent sequences: A340057 A340058 A340059 * A340061 A340062 A340063

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Dec 27 2020

Status

approved