OFFSET
1,1
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)=2x. But for these many solutions x, both numbers x-n and x+n are primes.
EXAMPLE
a(1)=11 because 11-1 is composite, phi(11+1)+sigma(11-1)=2*11 and there is no such number less than 11.
MATHEMATICA
a[n_]:=(For[m=n+1, PrimeQ[m-n]||EulerPhi[m+n]+DivisorSigma[1, m-n]!=2m, m++]; m); Table[a[n], {n, 70}]
PROG
(PARI)
a(n)=m=n+4; while(isprime(m-n)||eulerphi(m+n)+sigma(m-n)!=2*m, 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