A277908 -id:A277908 - cp's OEIS frontend

A277907 a(n) = A007310(A277908(n)).

5, 7, 11, 13, 17, 19, 41, 43, 59, 61, 67, 71, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 179, 181, 191, 193, 197, 199, 227, 229, 269, 271, 277, 281, 307, 311, 313, 317, 347, 349, 379, 383, 419, 421, 431, 433, 439, 443, 461, 463, 487, 491, 499, 503, 599, 601, 617, 619, 643, 647, 739, 743, 823, 827, 853, 857, 859, 863, 877, 881

Offset: 1

Antti Karttunen, Nov 05 2016

nonn

It seems that all terms are primes, and moreover, that all those primes occur in pairs with distance of 2 or 4. However, not all terms of A001359 are present.

Antti Karttunen, Table of n, a(n) for n = 1..7096

Cf. A000040, A001359, A007310, A118306, A277908, A277911.

(define (A277907 n) (A007310 (A277908 n)))

a(n) = A007310(A277908(n)).

A277911 Self-inverse permutation of natural numbers induced when A118306 is restricted to A007310.

Original entry on oeis.org

1, 3, 2, 5, 4, 7, 6, 10, 17, 8, 13, 26, 11, 15, 14, 18, 9, 16, 31, 21, 20, 40, 24, 23, 27, 12, 25, 30, 45, 28, 19, 54, 34, 33, 36, 35, 38, 37, 68, 22, 57, 115, 44, 43, 29, 47, 46, 74, 73, 51, 50, 87, 55, 32, 53, 58, 41, 56, 180, 61, 60, 96, 83, 65, 64, 67, 66, 39, 101, 100, 75, 110, 49, 48, 71, 77, 76, 80, 124, 78, 84, 283, 63, 81, 126, 88, 52

Offset: 1

Antti Karttunen, Nov 05 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10001
Index entries for sequences that are permutations of the natural numbers

Cf. A007310, A118306, A126760.

Cf. A277908, A277909, A277910 (for "almost fixed points"), also A277907.

A118306(n) = { if(1==n, 1, my(f = factor(n)); my(d = (-1)^primepi(f[1, 1])); for(i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-d)); factorback(f)); };
A007310(n) = n\2*6-(-1)^n; \\ From M. F. Hasler, Oct 31 2014
A126760(n) = {n&&n\=3^valuation(n, 3)<M. F. Hasler, Jan 19 2016
A277911(n) = A126760(A118306(A007310(n)));
for(n=1, 10001, write("b277911.txt", n, " ", A277911(n)));

(define (A277911 n) (A126760 (A118306 (A007310 n))))

a(n) = A126760(A118306(A007310(n))).

A277909 Numbers n for which A277911(n) = n+1.

Original entry on oeis.org

2, 4, 6, 14, 20, 23, 33, 35, 37, 43, 46, 50, 60, 64, 66, 76, 90, 93, 103, 105, 116, 127, 140, 144, 147, 154, 163, 167, 200, 206, 215, 247, 275, 285, 287, 293, 295, 303, 313, 323, 337, 340, 344, 363, 365, 410, 427, 430, 433, 435, 440, 476, 483, 495, 497, 523, 527, 533, 536, 555, 566, 596, 623, 625, 665, 667, 676, 694, 696, 714, 747, 757

Offset: 1

Antti Karttunen, Nov 05 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..481

Odd bisection of A277908.
One less than A277910.
Cf. A277911.

A277910 Numbers n for which A277911(n) = n-1.

Original entry on oeis.org

3, 5, 7, 15, 21, 24, 34, 36, 38, 44, 47, 51, 61, 65, 67, 77, 91, 94, 104, 106, 117, 128, 141, 145, 148, 155, 164, 168, 201, 207, 216, 248, 276, 286, 288, 294, 296, 304, 314, 324, 338, 341, 345, 364, 366, 411, 428, 431, 434, 436, 441, 477, 484, 496, 498, 524, 528, 534, 537, 556, 567, 597, 624, 626, 666, 668, 677, 695, 697, 715, 748, 758

Offset: 1

Antti Karttunen, Nov 05 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..481

Even bisection of A277908.
One more than A277909.
Cf. A277911.

a(n) = 1 + A277909(n).

cp's OEIS Frontend

A277907 a(n) = A007310(A277908(n)).

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A277911 Self-inverse permutation of natural numbers induced when A118306 is restricted to A007310.

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A277909 Numbers n for which A277911(n) = n+1.

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A277910 Numbers n for which A277911(n) = n-1.

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