A321795 -id:A321795 - cp's OEIS frontend

A321985 Numbers m such that m^2+1 is semiprime with (m-1)^2+1 and (m+1)^2+1 primes.

3, 5, 15, 25, 205, 715, 1095, 1315, 1615, 2055, 2405, 2925, 3755, 4615, 4795, 5015, 5055, 5475, 6785, 7855, 8115, 8175, 9425, 9475, 10415, 10845, 11025, 11245, 12335, 12765, 15225, 16225, 16395, 16405, 18145, 18175, 18275, 21345, 21915, 22905, 23165, 23815

Offset: 1

Michel Lagneau, Nov 23 2018

nonn

Subsequence of A085722.
For n>1, a(n) == 5 (mod 10).
The corresponding pairs of primes (p, q) = ((m-1)^2+1, (m+1)^2+1) are congruent to 7 (mod 10), and the semiprimes are of the form m^2+1 = 2r where r is congruent to 3 (mod 10). So, a(n) = (q - 2r - 1)/2 = (2r - p + 1)/2 = (q - p)/4.

			15 is in the sequence because 15^2 + 1 = 2*113 is semiprime, and 14^2 + 1 = 197, 16^2 + 1 = 257 are prime numbers.

Cf. A005574, A085722, A321795.

Select[Range[50000],PrimeQ[(#-1)^2+1]&&PrimeOmega [#^2+1]==2&&PrimeQ[(#+1)^2+1]&]

isok(m) = (bigomega(m^2+1) == 2) && isprime((m-1)^2+1) && isprime((m+1)^2+1); \\ Michel Marcus, Nov 23 2018

cp's OEIS Frontend

A321985 Numbers m such that m^2+1 is semiprime with (m-1)^2+1 and (m+1)^2+1 primes.

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