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URL: https://oeis.org/A054906

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A054906
Smallest number x such that sigma(x+2n) = sigma(x)+2n (first definition).
7
3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 7, 5, 3, 3, 7, 5, 3, 5, 3, 3, 5, 3, 7, 5, 3, 7, 5, 3, 3, 7, 5, 3, 5, 3, 3, 7, 5, 3, 5, 3, 7, 5, 3, 13, 7, 5, 3, 5, 3, 3, 5, 3, 3, 5, 3, 19, 13, 11, 13, 7, 5, 3, 5, 3, 7, 5, 3, 3, 11, 11, 7, 5, 3, 3, 7, 5, 3, 7, 5, 3, 5, 3, 7, 5, 3, 7, 5, 3, 3, 11, 11, 7, 5, 3, 3, 5, 3, 3, 13
OFFSET
1,1
COMMENTS
Least (prime) solutions for phi(x+2n)=phi(x)+2n seems to be identical to this sequence, while prime solutions are indeed identical to this sequence.
2nd definition = smallest number x such that phi(x+2n)=phi(x)+2n.
3rd definition = smallest primes p such that p+2n=q prime (A020483).
The 3 definitions are identical or conjectured to be identical.
The definitions are not identical if we do not take the smallest numbers. These smallest solutions are believed to be always prime numbers.
Duplicate of A020483, assuming that the 3rd definition is also correct. - R. J. Mathar, Apr 26 2015
If it can be proved that all these definitions are identical, then this entry should be merged with A020483. - N. J. A. Sloane, Feb 06 2017
REFERENCES
Sivaramakrishnan,R.(1989):Classical Theory of Arithmetical Functions. Marcel Dekker,Inc., New York.
LINKS
FORMULA
Minimal solutions to A000203(x+2n)=A000203(x)+2n or to A000010(x+2n)=A000010(x)+2n or to p+2n=q; p, q primes, a(n)=p.
a(n) <= A054905(n). - R. J. Mathar, Apr 28 2015
EXAMPLE
n-th primes 2,3,5,7,11,13, are solutions to sigma(x+2n)=2n+sigma(x) at 2n=2,6,22,116,88.
MAPLE
A054906 := proc(n)
local x;
for x from 0 do
if numtheory[sigma](x+2*n) = numtheory[sigma](x)+2*n then
return x;
end if;
end do:
end proc:
seq(A054906(n), n=1..40); # R. J. Mathar, Sep 23 2016
MATHEMATICA
Table[x = 1; While[DivisorSigma[1, x + 2 n] != DivisorSigma[1, x] + 2 n, x++]; x, {n, 100}] (* Michael De Vlieger, Feb 05 2017 *)
PROG
(PARI) a(n) = my(x = 1); while(sigma(x+2*n) != sigma(x)+2*n, x++); x; \\ Michel Marcus, Dec 17 2013
KEYWORD
nonn
AUTHOR
Labos Elemer, May 23 2000
STATUS
approved