

A247011


Numbers n for which A242719(n) = (prime(n) + 2)^2 + 1.


5



5, 7, 13, 17, 26, 33, 64, 81, 98, 140, 171, 176, 190, 201, 215, 225, 318, 332, 336, 444, 469, 475, 495, 551, 558, 563, 577, 601, 636, 671, 828, 849, 862, 870, 948, 1004, 1064, 1074, 1189, 1198, 1230, 1238, 1305, 1328, 1445, 1449, 1528, 1618, 1634, 1642, 1679
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OFFSET

1,1


COMMENTS

(prime(n) + 2)^2 + 1 is the second minimal possible value of A242719(n) after prime(n)^2 + 1. Indeed, by the definition lpf(A242719(n)  3) > lpf(A242719(n)  1) >= prime(n), thus after prime(n)^2 + 1 we should consider prime(n)*(prime(n) + 2) + 1. Then prime(n) should be lesser number of twin primes, but then prime(n) + 1 == 0 (mod 3). So, prime(n)*(prime(n) + 2)  2 == 0 (mod 3). Analogously one can prove that prime(n)*(prime(n) + 4)  2 == 0 (mod 3).
Note that for the sequence prime(n+1) is in intersection of A006512 and A062326, but prime(n) is not in A062326.


LINKS

François Marques, Table of n, a(n) for n = 1..109


FORMULA

If prime(n) is not in A062326, then A242719(n) >= (prime(n)+2)^2 + 1.
Intersection of A247011 and A246824 forms sequence 81, 215, 828, 1189, 1634, ... For these values of n we have A242719(n)  A242720(n) = 2*(prime(n) + 1).


CROSSREFS

Cf. A242719, A246748.
Sequence in context: A178218 A314323 A314324 * A172480 A285886 A106069
Adjacent sequences: A247008 A247009 A247010 * A247012 A247013 A247014


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Sep 09 2014


EXTENSIONS

More terms from Peter J. C. Moses, Sep 09 2014


STATUS

approved



