OFFSET
1,1
COMMENTS
a(2) = 0 since it is impossible.
LINKS
Daniel Suteu, Table of n, a(n) for n = 1..500 (terms 1..38 from Amiram Eldar)
EXAMPLE
a(5) = 53 because (53 + 59) = 112 = 2^4*7.
a(24) = 63700991 because (63700991 + 63700993) = 127401984 = 2^19*3^5.
a(28) = 3875536883 because (3875536883 + 3875536909) = 7751073792 = 2^25*3*7*11.
a(29) = 1358954453 because (1358954453 + 1358954539) = 2717908992 = 2^25*3^4.
a(30) = 1879048183 because (1879048183 + 1879048201) = 3758096384 = 2^29*7.
MATHEMATICA
f[n_] := Plus @@ Flatten[ Table[ #[[2]], {1}] & /@ FactorInteger[n]]; t = Table[0, {40}]; Do[a = f[Prime[n] + Prime[n + 1]]; If[a < 41 && t[[a]] == 0, t[[a]] = Prime[n]; Print[{a, Prime[n]}]], {n, 111500000}]; t
PROG
(PARI)
almost_primes(A, B, n) = A=max(A, 2^n); (f(m, p, n) = my(list=List()); if(n==1, forprime(q=max(p, ceil(A/m)), B\m, listput(list, m*q)), forprime(q=p, sqrtnint(B\m, n), list=concat(list, f(m*q, q, n-1)))); list); vecsort(Vec(f(1, 2, n)));
a(n) = if(n==2, return(0)); my(x=2^n, y=2*x); while(1, my(v=almost_primes(x, y, n)); for(k=1, #v, my(p=precprime(max(v[k]>>1, 2)), q=nextprime(p+1)); if(p+q == v[k], return(p))); x=y+1; y=2*x); \\ Daniel Suteu, Aug 06 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Giovanni Teofilatto and Robert G. Wilson v, Apr 06 2005
EXTENSIONS
a(28)=3875536883 from Ray Chandler and Robert G. Wilson v, Apr 10 2005
Edited by Ray Chandler, Apr 10 2005
a(31)-a(33) from Daniel Suteu, Nov 18 2018
Definition slightly modified by Harvey P. Dale, Jul 17 2024
STATUS
approved