A135284 Sum of staircase twin primes according to the rule: top + bottom - next top.

3, 1, 7, 7, 19, 25, 49, 43, 97, 79, 127, 121, 169, 187, 169, 217, 211, 259, 253, 277, 277, 409, 403, 403, 475, 541, 583, 595, 625, 511, 799, 817, 799, 835, 745, 1009, 1015, 1039, 1033, 1033, 1075, 1183, 1267, 1279, 1285, 1213, 1405, 1423, 1477, 1369, 1597, 1573

Offset

1,1

Comments

The case for bottom - top + next top produces A006512(n+1), the upper twin primes > 5.

Links

Table of n, a(n) for n=1..52.

Formula

We list the twin primes in staircase fashion as in A135283. Then a(n) = tl(n) + tu(n) + (-tl(n+1)).

a(n) = A054735(n)-A001359(n+1). - R. J. Mathar, Sep 10 2016

Prog

(PARI) g(n) = for(x=1, n, y=twinu(x) + twinl(x) - twinl(x+1); print1(y", ")) twinl(n) = / *The n-th lower twin prime. */ { local(c, x); c=0; x=1; while(c<n, if(ispseudoprime(prime(x)+2), c++); x++; ); return(prime(x-1)) } twinu(n) = /* The n-th upper twin prime. */ { local(c, x); c=0; x=1; while(c<n, if(isprime(prime(x)+2), c++); x++; ); return(prime(x)) }

Crossrefs

Sequence in context: A319298 A101748 A058606 * A016647 A091039 A217594

Adjacent sequences: A135281 A135282 A135283 * A135285 A135286 A135287

Keyword

nonn

Author

Cino Hilliard, Dec 03 2007

Status

approved