A135286 Sum of staircase twin primes according to the rule: top * bottom + next top.

20, 46, 160, 352, 940, 1822, 3670, 5284, 10510, 11800, 19192, 22678, 32590, 37060, 39430, 52222, 57868, 73180, 79834, 97690, 121522, 176830, 187084, 213964, 273052, 325498, 360616, 382564, 412822, 436408, 656920, 676510, 686440, 737044, 778942, 1041430, 1066072, 1103560, 1128934, 1193614, 1328332, 1514176, 1634572, 1665400, 1696522, 1743826, 2040634, 2109784, 2197810, 2215750

Offset

1,1

Comments

While there is multiplication 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..50.

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: A145220 A234266 A234259 * A338235 A177725 A264444

Adjacent sequences: A135283 A135284 A135285 * A135287 A135288 A135289

Keyword

nonn

Author

Cino Hilliard, Dec 03 2007

Extensions

All the entries were wrong. They have been corrected by Franklin T. Adams-Watters, Apr 29 2008

Status

approved