A265326 n-th prime minus its binary reversal.

1, 0, 0, 0, -2, 2, 0, -6, -6, 6, 0, -4, 4, -10, -14, 10, 4, 14, -30, -42, 0, -42, -18, 12, 30, 18, -12, 0, 18, 42, 0, -62, -8, -70, -20, -82, -28, -34, -62, -8, -26, 8, -62, 62, 34, -28, 8, -28, 28, 62, 82, -8, 98, 28, 0, -186, -84, -210, -60

Offset: 1

Author

Max Barrentine, Dec 07 2015

Keywords

• sign
• base
• look

Comments

a(n) = 0 iff A000040(n) is in A016041. - Altug Alkan, Dec 07 2015

The graph consists of a succession of parallelograms. The parallelograms end when there is a long run of mostly positive terms followed by a long run of mostly negative terms. The places where the successive parallelograms end are the primes just before a power of 2: 3, 7, 13, 31, 61, 127, 251, 509, 1021, 2039, 4093, 8191, 16381, 32749, ..., which are terms with indices 2, 4, 6, 11, 18, 31, 54, 97, 172, 309, 564, 1028, 1900, 3512, 6542, 12251, 23000, 43390, 82025, ... (see A014234 and A007053). - N. J. A. Sloane, May 29 2016

Examples

			n=5: prime(5) = 11_10 = 1011_2, reversing gives 1101_2 = 13_10, so a(5) = 11-13 = -2.
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..23000, May 29 2016 [First 10000 terms from _Robert Israel_]
• Rémy Sigrist, Colored scatterplot of the first 82025 terms (corresponding to the prime numbers < 2^20) (where the color is function of A000040(n) mod 8)
• N. J. A. Sloane, Table of n, a(n) for n = 1..78498
• N. J. A. Sloane and Brady Haran, Amazing Graphs, Numberphile video (2019)

Crossrefs

Cf. A055945, A068396, A098957, A007053, A014234.

Programs

Maple

revdigs:= proc(n) local L, j;
  L:= convert(n,base,2);
  add(L[-j]*2^(j-1),j=1..nops(L))
end proc:
map(t -> t - revdigs(t),  select(isprime, [2,seq(i,i=3..1000,2)])); # Robert Israel, Dec 08 2015

Mathematica

Table[# - FromDigits[Reverse@ IntegerDigits[#, 2], 2] &@ Prime@ n, {n, 60}] (* Michael De Vlieger, Dec 09 2015 *)

PARI

a098957(n) = my(v=binary(prime(n)), s); forstep(i=#v, 1, -1, s+=s+v[i]); s
a(n) = prime(n) - a098957(n); \\ Altug Alkan, Dec 07 2015

Formula

a(n) = A000040(n) - A098957(n).

a(n) = A055945(A000040(n)). - Michel Marcus, Dec 08 2015