OFFSET
0,1
COMMENTS
For each n, a(n) > n and like a(n)-n, a(n)+n is also composite.
If both numbers p and p + 2n are primes then x = p+n is a solution to the equation phi(x-n) + sigma(x+n) = phi(x+n) + sigma(x-n). But for these many solutions x, both numbers x-n and x+n are primes.
a(n) is the smallest integer m such that m-n is composite and A051612(m+n) = A051612(m-n) where A051612(n) = sigma(n) - phi(n). - Michel Marcus, Mar 20 2020
LINKS
Michel Marcus, Table of n, a(n) for n = 0..4501 (terms 0..1000 from Jinyuan Wang)
EXAMPLE
a(1)=153 because 153-1 is composite, phi(153-1)+sigma(153+1) = phi(153+1)+sigma(153-1) and there is no such number less than 153.
MATHEMATICA
a[0]=4; a[n_]:=a[n]=(For[m=n+1, PrimeQ[m-n]||EulerPhi[m-n]+DivisorSigma[1, m+n]!=EulerPhi[m+n]+DivisorSigma[1, m-n], m++]; m);
Table[a[n], {n, 0, 70}]
PROG
(PARI) a(n) = {my(m=n+4); while(isprime(m-n) || eulerphi(m+n)+sigma(m-n)!=eulerphi(m-n)+sigma(m+n), m++); m; }
vector(100, n, a(n)) \\ Derek Orr, Aug 30 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Jahangeer Kholdi and Farideh Firoozbakht, Aug 30 2014
STATUS
approved