A135285 Sum of staircase twin primes according to the rule: top * bottom - next top.

10, 24, 126, 294, 858, 1704, 3528, 5082, 10296, 11526, 18894, 22320, 32208, 36666, 38976, 51744, 57330, 72618, 79212, 96996, 120684, 175968, 186162, 212922, 271914, 324300, 359382, 381282, 411504, 434790, 655278, 674856, 684726, 735282, 776904

Offset

1,1

Comments

While there is multiplication and subtraction in the generation of this sequence, it is still called a sum because the arithmetic processes -,*,/ are derived from addition.

Links

Table of n, a(n) for n=1..35.

Formula

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

a(n) = A037074(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: A126911 A223408 A261807 * A235940 A103071 A264296

Adjacent sequences: A135282 A135283 A135284 * A135286 A135287 A135288

Keyword

nonn

Author

Cino Hilliard, Dec 03 2007

Status

approved