A376275 - OEIS

A376275

Semiprimes s such that (3s+1)/2 is semiprime and A001414(s)=2*A001414((3s+1)/2).

114239, 144059, 933899, 1918199, 25054499, 30495419, 33065159, 72602039, 255442559, 353104079, 575473559, 808589879, 846509819, 1042804799, 1055710979, 1059728279, 1184657879, 1247085239, 1791627599, 2196997739, 2323221179, 2372469179, 2591327159, 3063507719, 3276652079, 4021840859, 5489857619, 5716553879, 6022735799

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OFFSET

1,1

COMMENTS

Both a(n) and (3a(n)+1)/2 are odd.

Both a(n) and (3a(n)+1)/2 are congruent to 2 mod 3.

a(n) is congruent to 3 mod 4.

Both a(n) and (3a(n)+1)/2 are congruent to 4 mod 5 and the two prime factors are congruent to 1 and 4 mod 5.

Both a(n) and (3a(n)+1)/2 are congruent to 9 mod 10 and the two prime factors are congruent to 1 and 9 mod 10.

a(n) is also a solution to the arithmetic differential equation A003415((3m+1)/2)=A003415(m)/2.

If a(n) = p*(p-m), with p and p-m prime, then m>=2*sqrt(30p^2+2)-10p.

The sum of the reciprocals 1/a(n) converges.

LINKS

Table of n, a(n) for n=1..29.

CROSSREFS

Cf. A001358, A046315, A001414, A003415.

Sequence in context: A138266 A175697 A023092 * A221334 A069371 A143725

Adjacent sequences: A376272 A376273 A376274 * A376276 A376277 A376278

KEYWORD

nonn

AUTHOR

Zachary P. Bradshaw, Sep 18 2024

EXTENSIONS

One of the editors suggests that the following article is related: https://www.researchgate.net/publication/384084846_A_Family_of_Solutions_to_Arithmetic_Differential_Equations_Involving_the_Collatz_Map - N. J. A. Sloane, Oct 23 2024

STATUS

approved