A090456 -id:A090456

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A090455

Difference between numbers of binary 1's of n and binary 1's of n-th prime.

+10
6

0, -1, 0, -2, -1, -1, 1, -2, -2, -2, -2, -1, 0, -1, -1, -3, -3, -3, 0, -2, 0, -2, 0, -2, 0, -1, -1, -2, -1, 0, -2, -2, -1, -2, -1, -3, -2, -1, -1, -3, -2, -2, -3, 0, 0, -1, 0, -5, -2, -2, -1, -4, -1, -3, 3, -1, 0, -1, 1, 0, 0, 1, 1, -5, -3, -4, -2, -2, -3, -3, 0, -4, -4, -3

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

OFFSET

1,4

LINKS

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

FORMULA

a(n) = A000120(n) - A014499(n);

a(A071600(n)) = a(A049084(A072439(n))) = 0.

a(A049084(A090456(n))) < 0.

a(A049084(A090457(n))) > 0.

MATHEMATICA

Table[DigitCount[n, 2, 1]-DigitCount[Prime[n], 2, 1], {n, 80}] (* Harvey P. Dale, Aug 08 2013 *)

CROSSREFS

Cf. A000120, A014499.

Cf. A007088, A004676, A090431.

Cf. A049084, A071600, A090456, A090457.

KEYWORD

sign,base

AUTHOR

Reinhard Zumkeller, Dec 01 2003

EXTENSIONS

Definition clarified by Harvey P. Dale, Aug 08 2013

STATUS

approved

A090457

Primes prime(k) having fewer binary 1's than k.

+10
4

17, 257, 277, 293, 307, 401, 449, 577, 641, 643, 653, 673, 677, 709, 1031, 1033, 1039, 1091, 1093, 1129, 1153, 1217, 1297, 1409, 1543, 1553, 1601, 1607, 1609, 1613, 2053, 2063, 2081, 2083, 2087, 2089, 2099, 2113, 2179, 2309, 2341, 2371, 2593, 2609, 2633, 2647

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

OFFSET

1,1

LINKS

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

FORMULA

A090455(a(n)) > 0.

MATHEMATICA

seq[len_] := Module[{s = {}, p = 2, k = 1, c = 0}, While[c < len, If[Greater @@ DigitCount[{k, p}, 2, 1], c++; AppendTo[s, p]]; k++; p = NextPrime[p]]; s]; seq[50] (* Amiram Eldar, Jul 18 2023 *)

Prime[#]&/@Select[Range[500], DigitCount[#, 2, 1]>DigitCount[Prime[#], 2, 1]&] (* Harvey P. Dale, Apr 19 2024 *)

PROG

(PARI) isok(k) = hammingweight(prime(k)) < hammingweight(k);

lista(nn) = for(n=1, nn, if (isok(n), print1(prime(n), ", "))); \\ Michel Marcus, Feb 05 2016

CROSSREFS

Cf. A000120, A004676, A072439, A014499, A007088, A090433, A090455, A090456.

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Dec 01 2003

STATUS

approved

A090432

Primes prime(k) having a greater sum of digits than does k.

+10
3

2, 3, 5, 7, 17, 19, 29, 31, 37, 41, 43, 47, 53, 59, 67, 71, 73, 79, 83, 89, 97, 113, 127, 137, 139, 149, 157, 167, 173, 179, 181, 191, 193, 197, 199, 229, 233, 239, 257, 269, 277, 281, 283, 293, 307, 349, 353, 359, 367, 373, 379, 383, 389, 397, 409, 419, 439

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

OFFSET

1,1

COMMENTS

A090431(a(n)) < 0.

LINKS

Table of n, a(n) for n=1..57.

MATHEMATICA

Prime[#]&/@Select[Range[100], Total[IntegerDigits[Prime[#]]]-Total[IntegerDigits[#]]>0&] (* Michel Lagneau, Nov 07 2015 *)

PROG

(PARI) isok(n) = sumdigits(prime(n)) > sumdigits(n); \\ Michel Marcus, Nov 07 2015

CROSSREFS

Cf. A007605, A007953, A033548, A090431, A090433, A090456.

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Dec 01 2003

STATUS

approved

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