cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A338454 Starts of runs of 4 consecutive numbers with the same total binary weight of their divisors (A093653).

Original entry on oeis.org

242, 947767, 1041607, 2545015, 3275463, 8170983, 15720871, 21532430, 23752181, 25135885, 25595913, 27981703, 28226983, 30505142, 30962767, 33364805, 37264493, 49002661, 49766629, 52910454, 53408456, 57917191, 57952016, 58331576, 59230454, 60014053, 60723111, 63378005
Offset: 1

Views

Author

Amiram Eldar, Oct 28 2020

Keywords

Comments

Numbers k such that A093653(k) = A093653(k+1) = A093653(k+2) = A093653(k+3).

Examples

			242 is a term since A093653(242) = A093653(243) = A093653(244) = A093653(245) = 18.
		

Crossrefs

Cf. A093653.
Subsequence of A338452 and A338453.
Similar sequences: A006601, A045932, A045940.

Programs

  • Mathematica
    f[n_] := DivisorSum[n, DigitCount[#, 2, 1] &]; s = {}; m = 4; fs = f /@ Range[m]; Do[If[Equal @@  fs, AppendTo[s, n - m]]; fs = Rest @ AppendTo[fs, f[n]], {n, m + 1, 10^7}]; s

A338515 Starts of runs of 3 consecutive numbers that are divisible by the total binary weight of their divisors (A093653).

Original entry on oeis.org

1, 348515, 8612344, 29638764, 30625110, 32039808, 32130600, 32481682, 43664313, 55318282, 55503719, 59671714, 69254000, 73152296, 93470904, 100366594, 103640097, 105026790, 109038462, 109212287, 122519464, 126667271, 147208982, 162007166, 169237545, 173392238
Offset: 1

Views

Author

Amiram Eldar, Oct 31 2020

Keywords

Examples

			1 is a term since 1, 2 and 3 are terms of A093705.
		

Crossrefs

Subsequence of A338514.
Similar sequences: A154701, A330932, A334346, A338453.

Programs

  • Mathematica
    divQ[n_] := Divisible[n, DivisorSum[n, DigitCount[#, 2, 1] &]]; div = divQ /@ Range[3]; Reap[Do[If[And @@ div, Sow[k - 3]]; div = Join[Rest[div], {divQ[k]}], {k, 4, 10^7}]][[2, 1]]

A338455 Starts of runs of 5 consecutive numbers with the same total binary weight of their divisors (A093653).

Original entry on oeis.org

1307029927, 2116078861, 2665774183, 2809370965, 4108623302, 4493733751, 5333670902, 5497285284, 5679049670, 8209799382, 9665369455, 9708528486, 10353426151, 10606564910, 12777118615, 12795699493, 13660293367, 13847206214, 14351020663, 15735895813, 17912257013
Offset: 1

Views

Author

Amiram Eldar, Oct 28 2020

Keywords

Comments

Numbers k such that A093653(k) = A093653(k+1) = A093653(k+2) = A093653(k+3) = A093653(k+4).
Can 6 consecutive numbers have the same total binary weight of their divisors? If they exist, then they are larger than 10^11.

Examples

			1307029927 is a term since A093653(1307029927) = A093653(1307029928) = A093653(1307029929) = A093653(1307029930) = A093653(1307029931) = 72.
		

Crossrefs

Cf. A093653.
Subsequence of A338452, A338453 and A338454.
Similar sequences: A045933, A045941, A049051.

Programs

  • Mathematica
    f[n_] := DivisorSum[n, DigitCount[#, 2, 1] &]; s = {}; m = 5; fs = f /@ Range[m]; Do[If[Equal @@  fs, AppendTo[s, n - m]]; fs = Rest @ AppendTo[fs, f[n]], {n, m + 1, 10^7}]; s

A339551 Starts of runs of 3 consecutive numbers with the same product of the binary weights of their divisors (A339549).

Original entry on oeis.org

513059433, 3007912105, 4791685641, 11555664153, 44615854297, 111890605585, 121111724905, 163901238153
Offset: 1

Views

Author

Amiram Eldar, Dec 08 2020

Keywords

Comments

Analogous to A338453 as A339549 is analogous to A093653.

Examples

			513059433 is a term since A339549(513059433) = A339549(513059434) = A339549(513059435) = 1166400.
		

Crossrefs

Subsequence of A339550.

Programs

  • Mathematica
    f[n_] := Times @@ (DigitCount[#, 2, 1] & /@ Divisors[n]); s = {}; m = 3; fs = f /@ Range[m]; Do[If[Equal @@  fs, AppendTo[s, n - m]]; fs = Rest @ AppendTo[fs, f[n]], {n, m + 1, 5*10^9}]; s
Showing 1-4 of 4 results.