A108568 -id:A108568 - cp's OEIS frontend

A108562 Primes of the form prime(n) + prime(n+1) - 2n - 1.

2, 3, 5, 13, 17, 53, 61, 79, 103, 109, 137, 151, 163, 179, 229, 271, 277, 317, 353, 409, 419, 431, 439, 443, 491, 499, 547, 557, 569, 593, 619, 631, 641, 677, 719, 811, 887, 937, 997, 1009, 1021, 1051, 1063, 1091, 1201, 1229, 1249, 1259, 1307, 1327, 1367

Offset: 1

Giovanni Teofilatto, Jul 05 2005

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A108568.

Select[(#[[3]]+#[[2]]-2#[[1]]-1)&/@(Join[{PrimePi[#[[1]]]},#]&/@ Partition[ Prime[Range[200]],2,1]),PrimeQ] (* Harvey P. Dale, Sep 07 2012 *)

Extended by Ray Chandler, Jul 10 2005

A108567 a(0) = 0, a(1) = a(2) = 1, a(3) = 2, a(4) = 4, a(5) = 8, a(6) = 16, for n>5: a(n+1) = SORT[ a(n) + a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6)], where SORT places digits in ascending order and deletes 0's.

Original entry on oeis.org

0, 1, 1, 2, 4, 8, 16, 23, 55, 19, 127, 225, 347, 128, 249, 115, 112, 133, 139, 1223, 299, 227, 2248, 1348, 1567, 157, 679, 2556, 2788, 11334, 2249, 1233, 2699, 23358, 12467, 12568, 5689, 2366, 368, 15559, 23577, 24579, 4678, 16678, 5788, 12279, 11338

Offset: 0

Jonathan Vos Post, Jun 11 2005

T. D. Noe found that the maximum is attained at a(4992871827) = 234444568999. The periodic part of this sequence begins at a(3544675600) and has length 5158842780.

			a(7) = SORT[a(0) + a(1) + a(2) + a(3) + a(4) + a(5) + a(6)] = SORT[0 + 1 + 1 + 2 + 4 + 8 + 16] = SORT[32] = 23.
a(8) = SORT[a(1) + a(2) + a(3) + a(4) + a(5) + a(6) + a(7)] = SORT[1 + 1 + 2 + 4 + 8 + 16 + 23] = SORT[55] = 55.
a(9) = SORT[a(2) + a(3) + a(4) + a(5) + a(6) + a(7) + a(8)] = SORT[1 + 2 + 4 + 8 + 16 + 23 + 55] = SORT[109] = 19.

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Richard I. Hess, Problem 920: sorted Fibonacci sequence, Pi Mu Epsilon Journal, Vol. 10 (Fall 1998) No. 9, pp. 754-755.

Cf. A066178, A069638, A107281, A108564-A108566, A108568-A108573.

nxt[{a_,b_,c_,d_,e_,f_,g_}]:={b,c,d,e,f,g,FromDigits[Sort[ IntegerDigits[ a+b+c+d+e+f+g]/.(0->Nothing)]]}; NestList[nxt,{0,1,1,2,4,8,16},50][[All,1]] (* Harvey P. Dale, May 09 2020 *)

cp's OEIS Frontend

A108562 Primes of the form prime(n) + prime(n+1) - 2n - 1.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions