A095743 -id:A095743 - cp's OEIS frontend

A095753 Number of almost base-2 palindromic primes (A095743) in range ]2^n,2^(n+1)].

0, 0, 2, 3, 5, 4, 15, 18, 32, 33, 63, 81, 119, 144, 256, 318, 527, 640, 1029, 1281, 2236, 2566, 4273, 5410, 8261, 10610, 16868, 21084, 33943, 43104, 68218, 88493, 136343

Offset: 1

Antti Karttunen, Jun 12 2004

Ratio a(n)/A036378(n) converges as follows: 0, 0, 1, 0.6, 0.714286, 0.307692, 0.652174, 0.418605, 0.426667, 0.240876, 0.247059, 0.174569, 0.136468, 0.08933, 0.084488, 0.055702, 0.049028, 0.031388, 0.026634, 0.017408, 0.015933, 0.009567, 0.008318, 0.005488, 0.004361, 0.00291, 0.0024, 0.001555, 0.001295, 0.00085, 0.000695, 0.000465, 0.000369

Ratio a(n)/A095758(n) converges as follows: 1, 1, 0, 1.5, 1, 1, 3.75, 1.2, 2, 1.375, 1.909091, 1.446429, 1.652778, 1.515789, 1.718121, 1.452055, 1.636646, 1.191806, 1.570992, 1.283567, 1.708174, 1.380312, 1.534842, 1.392177, 1.547004, 1.311334, 1.573801, 1.302205, 1.521016, 1.419202, 1.570938, 1.389237, 1.546084

The second diagonal of triangle A095759. Cf. A095742.

A095749 Square array A(row>=1, col>=1) by antidiagonals: A(r,c) contains the c:th prime p for which A037888(p)=(r-1).

Original entry on oeis.org

3, 5, 2, 7, 11, 43, 17, 13, 53, 151, 31, 19, 71, 179, 599, 73, 23, 79, 233, 683, 2111, 107, 29, 83, 241, 739, 2143, 8543, 127, 37, 101, 271, 797, 2503, 9103, 33023, 257, 41, 109, 311, 853, 2731, 9623, 33151, 131839, 313, 47, 113, 331, 937, 3011, 10427, 33599, 135647, 531071

Offset: 1

Antti Karttunen, Jun 12 2004

			a(1) = A(1,1) = 3 (11 in binary) as it is the first prime whose binary expansion is palindromic. a(2) = A(1,2) = 5 (101 in binary) as it is the second prime whose binexp is palindromic. a(3) = A(2,1) = 2 (10 in binary) as it is the first prime whose binexp needs a flip of just one bit to become palindrome. a(4) = A(1,3) = 7 (111 in binary) as it is the third prime whose binexp is palindromic. a(5) = A(2,2) = 11 (1011 in binary) as it is the second prime whose binexp needs a flip of just one bit to become palindrome.

Row 1: A016041, 2: A095743, 3: A095744, 4: A095745, 5: A095746. Cf. also A095759. A095747-A095748. Permutation of primes (A000040).

A095748 Almost maximally asymmetric primes in binary.

Original entry on oeis.org

17, 31, 37, 41, 47, 59, 61, 67, 89, 97, 103, 139, 149, 163, 197, 263, 269, 283, 293, 307, 353, 359, 379, 389, 409, 433, 439, 449, 461, 499, 541, 557, 607, 613, 631, 659, 727, 743, 809, 829, 877, 929, 941, 953, 997, 1009, 1039, 1051, 1151, 1171

Offset: 1

Antti Karttunen, Jun 12 2004

Primes p for which A037888(p) = floor((A070939(p)-4)/2). Those numbers contain just two bits mirroring each other, beyond the first and last bits. (All the odd primes without leading zeros begin and end in 1 bits.)

			a(5)=(101111)2. In this case, from left to right, the third bit agrees with the fourth. The prime 53 = (110101)_2 is not a term since the symmetry is limited to the first and last bits.

A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence

Cf. A095758, A095749, A095743.

A070939(p) = { return(floor(log(p)/log(2))+1) };
A037888(p)={v=binary(p);s=0;j=#v;for(k=1,#v,s+=abs(v[k]- v[j]);j--);return(s/2);}; forprime(p=3,1171,if(A037888(p)==floor((A070939(p)-4)/2), print1(p,", ")))

Edited by Washington Bomfim, Jan 13 2011

cp's OEIS Frontend

A095753 Number of almost base-2 palindromic primes (A095743) in range ]2^n,2^(n+1)].

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A095749 Square array A(row>=1, col>=1) by antidiagonals: A(r,c) contains the c:th prime p for which A037888(p)=(r-1).

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A095748 Almost maximally asymmetric primes in binary.

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