A368404 -id:A368404

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A368402

Numbers k such that k and k+1 are both in A268375.

+10
3

1, 2, 3, 4, 7, 8, 11, 12, 16, 17, 18, 19, 27, 28, 31, 43, 44, 47, 48, 49, 52, 63, 67, 75, 79, 80, 97, 98, 112, 116, 124, 127, 147, 148, 162, 163, 171, 172, 175, 191, 192, 207, 211, 241, 242, 243, 244, 256, 268, 271, 283, 288, 292, 316, 324, 331, 332, 337, 367

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Analogous to A342028, as A268375 is analogous to A130091.

The Mersenne primes (A000668) are terms.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

MATHEMATICA

f[e_] := Position[Reverse[IntegerDigits[e, 2]], 1] // Flatten; q[n_] := q[n] = UnsameQ @@ Flatten[f /@ FactorInteger[n][[;; , 2]]]; Select[Range[100], q[#] && q[#+1] &]

PROG

(PARI) isA268375(n) = {my(e = factor(n)[, 2], b = 0); for(i=1, #e, b = bitor(b, e[i])); n == 1 || b == vecsum(e); }

lista(kmax) = {my(is1 = 0, is2); for(k = 1, kmax, is2 = isA268375(k); if(is1 && is2, print1(k-1, ", ")); is1 = is2); }

CROSSREFS

Subsequence of A130091, A268375 and A342028.

Subsequences: A000668, A368403, A368404.

KEYWORD

nonn,base

AUTHOR

Amiram Eldar, Dec 23 2023

STATUS

approved

A368403

Starts of runs of 3 consecutive integers in A268375.

+10
3

1, 2, 3, 7, 11, 16, 17, 18, 27, 43, 47, 48, 79, 97, 147, 162, 171, 191, 241, 242, 243, 331, 367, 387, 431, 507, 547, 603, 907, 1051, 1249, 1250, 1619, 1871, 2267, 2347, 2523, 2799, 3411, 3643, 3987, 4049, 4050, 4111, 4175, 4203, 4491, 4923, 5119, 5391, 5407, 6091

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Analogous to A342029, as A268375 is analogous to A130091.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

MATHEMATICA

f[e_] := Position[Reverse[IntegerDigits[e, 2]], 1] // Flatten; q[n_] := UnsameQ @@ Flatten[f /@ FactorInteger[n][[;; , 2]]]; q[0] = False; seq[kmax_] := Module[{m = 3, s = {}, v}, v = q /@ Range[0, m - 1]; Do[v = Join[Rest[v], {q[k]}]; If[And @@ v, AppendTo[s, k - m + 1]], {k, m, kmax}]; s]; seq[6000]

PROG

(PARI) isA268375(n) = {my(e = factor(n)[, 2], b = 0); for(i=1, #e, b = bitor(b, e[i])); n == 1 || b == vecsum(e); }

lista(kmax) = {my(tri = vector(3, i, isA268375(i)), k = 4); while(k < kmax, if(vecsum(tri) == 3, print1(k-3, ", ")); tri = concat(vecextract(tri, "^1"), isA268375(k)); k++); }

CROSSREFS

Subsequence of A130091, A268375, A342029 and A368402.

A368404 is a subsequence.

KEYWORD

nonn,base

AUTHOR

Amiram Eldar, Dec 23 2023

STATUS

approved

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