A090433 -id:A090433 - cp's OEIS frontend

A090431 Difference between sums of digits of n and n-th prime.

-1, -1, -2, -3, 3, 2, -1, -2, 4, -10, -2, -7, -1, -2, -5, -1, -6, 2, -3, -6, -7, -12, -6, -11, -9, 6, 5, 2, 1, -2, -6, 0, -5, -6, -6, 2, -3, 1, -2, -7, -12, -4, -4, -5, -8, -9, 7, 5, 2, -8, -2, -7, 1, 1, -4, 0, -5, 3, -2, -5, -6, -6, -1, 5, 4, 1, 6, 1, 1, -9, -3, -8, -6, -2

Offset: 1

Reinhard Zumkeller, Dec 01 2003

a(n) = A007953(n) - A007605(n);

a(A033549(n))=a(A049084(A033548(n)))=0; a(A049084(A090432(n)))<0; a(A049084(A090433(n)))>0.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A239324 (partial sums).

a090431 n = a007953 n - a007605 n  -- Reinhard Zumkeller, Mar 16 2014

A090457 Primes prime(k) having fewer binary 1's than k.

Original entry on oeis.org

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

Offset: 1

Reinhard Zumkeller, Dec 01 2003

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

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

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 *)

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

A090455(a(n)) > 0.

A090432 Primes prime(k) having a greater sum of digits than does k.

Original entry on oeis.org

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

Offset: 1

Reinhard Zumkeller, Dec 01 2003

A090431(a(n)) < 0.

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

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

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

cp's OEIS Frontend

A090431 Difference between sums of digits of n and n-th prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

A090457 Primes prime(k) having fewer binary 1's than k.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A090432 Primes prime(k) having a greater sum of digits than does k.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

PARI