A033548 -id:A033548 - cp's OEIS frontend

A259067 Sum of digits of Honaker primes (A033548).

5, 11, 16, 13, 14, 11, 5, 11, 11, 14, 14, 16, 8, 7, 14, 11, 17, 17, 16, 19, 20, 13, 16, 14, 16, 13, 22, 13, 14, 13, 19, 23, 14, 16, 16, 14, 17, 13, 14, 17, 14, 20, 23, 10, 11, 16, 17, 19, 20, 20, 23, 23, 23, 11, 13, 20, 13, 20, 17, 19, 10, 19, 13, 14, 16, 20, 10, 10, 13, 10, 13, 10, 13, 13, 19, 17, 13, 11, 14, 14, 14, 22, 16, 19, 20, 16, 20, 19, 20, 19, 20

Offset: 1

Zak Seidov, Jun 18 2015

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A007605, A007953, A033548, A033549.

lista(nn) = forprime(p=2, nn, if ((sd=sumdigits(p)) == sumdigits(primepi(p)), print1(sd, ", "));); \\ Michel Marcus, Jun 18 2015

go(lim)=my(v=List(),n,s);forprime(p=2,lim, s=sumdigits(n++); if(sumdigits(p)==s, listput(v,s))); Vec(v) \\ Charles R Greathouse IV, Jun 18 2015

a(n) = A007953(A033548(n)) = A007953(A033549(n)).

A151993 Number of Honaker primes (A033548) less than 10^n.

Original entry on oeis.org

0, 0, 3, 63, 410, 2949, 21622, 175504, 1478015, 12330087, 107585476, 937135794

Offset: 1

T. D. Noe, Sep 14 2009

G. L. Honaker, Jr. computed the first six terms. Are there an infinite number of Honaker primes?

			a(3) = 3 because 131, 263, and 457 are the only Honaker primes less than 10^3.

Cf. A006880 (primes < 10^n).

nn=6; cnt=0; power10=10; Reap[Do[p=Prime[k]; If[p>power10, Sow[cnt]; power10=10*power10]; If[Total[IntegerDigits[k]] == Total[IntegerDigits[p]], cnt++ ], {k,PrimePi[10^nn]+1}]][[2,1]]

A161118 Honaker emirps: terms in A033548 that are emirps.

Original entry on oeis.org

1091, 1301, 1913, 1933, 3067, 3433, 7481, 7523, 9103, 10247, 10429, 10711, 11071, 11353, 11701, 11731, 13297, 13457, 13933, 14447, 14843, 14923, 15263, 15803, 16073, 16193, 16451, 18013, 18041, 18307, 32009, 32261, 34471, 35027, 35129

Offset: 1

Lekraj Beedassy, Jun 02 2009

Intersection of A033548 and A006567. - Lekraj Beedassy, Jun 06 2009

Palindromic primes are not included. - Harvey P. Dale, Jun 13 2011

Cf. A006567, A033548.

nn=3800;emrpQ[n_]:=Module[{idn=IntegerDigits[n],ridn},ridn=Reverse[idn]; ridn!=idn && PrimeQ[FromDigits[ridn]]]; Select[Transpose[ Select[ Thread[ {Prime[Range[nn]],Range[nn]}], Total[IntegerDigits[First[#]]] == Total[IntegerDigits[Last[#]]]&]][[1]],emrpQ] (* Harvey P. Dale, Jun 13 2011 *)

Sequence corrected and extended by Lekraj Beedassy, Jun 06 2009

A161197 Smallest Honaker prime A033548 with digit sum prime(n), or 0 if no such prime exists.

Original entry on oeis.org

0, 0, 131, 2221, 263, 1039, 2591, 2719, 4397, 57089, 79609, 479881, 2557967, 1299499, 8796629, 49979249, 349929779, 753987769, 1397989867, 8278487999, 16874789779, 69355889899, 199785963989, 1787899947299, 17678888878867

Offset: 1

Lekraj Beedassy, Jun 06 2009

From Robert G. Wilson v, Jun 08 2009: (Start)
If instead the sequence is the least Honaker prime which digit sum a(n) then the terms would begin:
0, 0, 0, 0, 131, 0, 2221, 2141, 0, 6301, 263, 0, 1039, 1049, 0, 457, 2591, 0, 2719, 2729, 0, 3559, 4397, 0, 17359, 17189, 0, 37783, 57089, 0, 79609, 174767, 0, 324799, 349919, 0, 479881, 479783, 0, 879673, 2557967, 0, 1299499, 5487497, 0, 5487697, 8796629, 0, 14657899, 23879489, 0, 47678893, 49979249, 0, 67669687, 139579499, 0, 176937979, 349929779, 0, 753987769, 753987779, 0, 1397989819, 1397778887, 0, 1397989867, ..., . (End)
a(26) <= 29678788858889. - Donovan Johnson, Dec 29 2013

			The digit sums of A033548(n) are 5,11,16,13,14,11,5,11,11,14,14,16,8,7,14,11,17,17...
The first occurrence of the primes 5,7,11,13,... is at n=1,14,2,.., so the sequence displays A033548(1), A033548(14), A033548(2),...

Cf. A033548.

t = Table[0, {100}]; c = 1; p = 2; While[p < 35*10^8, a = Plus @@ IntegerDigits@ c; b = Plus @@ IntegerDigits@ p; If[a < 101 && a == b && t[[a]] == 0, t[[a]] = p; Print[{a, p}]]; c++; p = NextPrime@p]; t[[ # ]] & /@ Prime@ Range@ 19 (* Robert G. Wilson v, Jun 08 2009 *)

a(n) = min A033548(k): A007953(A033548(k)) = A000040(n). [R. J. Mathar, Jun 16 2009]

a(12)-a(19) from Robert G. Wilson v, Jun 08 2009
Simplified definition, added examples - R. J. Mathar, Jun 16 2009
a(20)-a(24) from Donovan Johnson, May 03 2010
a(25) from Donovan Johnson, Dec 29 2013

A033549 Numbers k such that sum of digits of k-th prime equals sum of digits of k.

Original entry on oeis.org

32, 56, 88, 175, 176, 182, 212, 218, 227, 248, 293, 295, 323, 331, 338, 362, 377, 386, 394, 397, 398, 409, 439, 446, 457, 481, 499, 508, 563, 571, 595, 599, 635, 637, 655, 671, 728, 751, 752, 755, 761, 767, 779, 820, 821, 826, 827, 847, 848, 857, 869, 878

Offset: 1

Calculated by Jud McCranie

A090431(a(n)) = 0, A007953(a(n)) = A007605(a(n)).

			131 is the 32nd prime and sum of digits of both is 5.

Proposed by G. L. Honaker, Jr.

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A033548, A071600.

a033549 n = a033549_list !! (n-1)
a033549_list = filter ((== 0) . a090431) [1..]
-- Reinhard Zumkeller, Mar 16 2014

Select[Range[1000],Total[IntegerDigits[#]]==Total[IntegerDigits[ Prime[#]]]&] (* Harvey P. Dale, May 05 2011 *)

is(n,p=prime(n))=sumdigits(n)==sumdigits(p) \\ Charles R Greathouse IV, Feb 07 2017

from sympy.ntheory.factor_ import digits
from sympy import prime
print([n for n in range(1, 1001) if sum(digits(n)[1:])==sum(digits(prime(n))[1:])]) # Indranil Ghosh, Jun 27 2017

A072439 Primes prime(k) such that the number of binary 1's in prime(k) equals the number of binary 1's in k.

Original entry on oeis.org

2, 5, 41, 67, 73, 83, 97, 113, 193, 197, 211, 269, 281, 283, 353, 389, 521, 523, 547, 563, 587, 593, 601, 647, 661, 691, 929, 937, 1061, 1063, 1097, 1109, 1117, 1123, 1289, 1319, 1361, 1381, 1489, 1549, 1559, 1567, 1571, 1579, 1597, 1801, 1873, 2069

Offset: 1

Reinhard Zumkeller, Jun 17 2002

			In binary representation 13 and A000040(13)=41 have three 1's: 13='1101' and 41='101001', therefore 41 is a term.

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

Cf. A000040, A000120, A014499, A033548, A049084, A071600, A090455.

Prime[Select[Range[400], DigitCount[#, 2, 1] == DigitCount[Prime[#], 2, 1] &]] (* Amiram Eldar, Aug 03 2023 *)

isok(p) = isprime(p) && ((hammingweight(p) == hammingweight(primepi(p)))); \\ Michel Marcus, Jun 14 2021

A000120(a(n)) = A000120(A071600(n)) = A014499(n).
A090455(A049084(a(n))) = 0.
a(n) = A000040(A071600(n)).

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

Original entry on oeis.org

-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

A176111 Honaker primes of the form p = 2*k-1 with sum-of-digits(p) = sum-of-digits(k).

Original entry on oeis.org

4357, 6301, 6553, 7741, 8011, 12277, 13339, 14437, 14923, 16273, 18307, 24733, 26731, 27091, 34471, 34543, 35227, 36217, 36307, 36433, 36523, 37783, 41491, 41851, 41941, 42373, 43543, 45181, 47017, 49411, 52543, 53407, 54217, 55207, 57943, 58321, 58411, 64513

Offset: 1

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 08 2010

The set of Honaker primes A033548 is intersected with the set {37, 73, 109, 127, 163, 181, 271, 307, 397, 433, 523, 541, 577, 613,...} of primes p = 2k-1, where A007953(p) = A007953(k) for the digit sums.
The requirement on the digit sum defining the Honaker primes plus the additional requirement on the digits sum of k means both digit sums are of the form 9*m+1, m>=1.
The sequence contains prime(n) for n = 595, 820, 847, 982, 1009, 1099, 1468, 15856, 1693, 1747,...
The fourth to sixth member of the sequence are three consecutive Honaker primes.
As a curiosity we have that for p=120709 = prime(11359) = A033548(469), k=60355 even the index in the Honaker primes has the same sum, 19.

			p = 2719 = prime(397) has digit sum 19, but k = 1360 has digit sum 10, which yields no term.
p = 6301 = prime(820) with k = 3151, digit sum 10, is the 2nd term.
p = 10711 = prime(1306) with digit sum 10, but k = 5356 has digit sum 10: no contribution to the sequence.
p = 57943 = prime(5869) with k = 28972 have common digit sum 28 and p is in the sequence.

M. du Sautoy: Die Musik der Primzahlen: Auf den Spuren des groessten Raetsels der Mathematik, Beck, 4. Auflage, 2005

Cf. A000040, A033548, A176012

4137 replaced by 4357, 8821 removed, Extensive list of auxiliary prime indices reduced - R. J. Mathar, Nov 01 2010

A177275 Primes which are a concatenation of some permutation of the first 5 primes.

Original entry on oeis.org

112573, 115237, 115327, 211573, 235117, 257311, 327511, 352711, 357211, 372511, 511237, 511327, 511723, 521137, 521173, 572311, 711523, 725113, 735211, 751123

Offset: 1

Ulrich Krug (leuchtfeuer37(AT)gmx.de), May 06 2010

There are 20 terms in the sequence. Each is a 6-digit prime with sum of digits equal to 19 = A051351(5).
For each of the 20 entries we define the index i via prime(i) = a(n), which yields the following 20 pairs of (i, A007953(i)):
(10668,21), (10892,20), (10901,11), (18940,22), (20845,19) HP,
(22622,14), (28208,20), (30192,15), (30538,19) HP, (31709,20),
(42386,23), (42392,20), (42426,18), (43145,17), (43149,21),
(47000,11), (57421,19) HP, (58426,25), (59175,27), (60315,15)
Where prime(i) is in A033548, this is marked as "HP" for "Honaker Prime".

			a(1) = 11//2//5//7//3 = 112573 = prime(10668).
a(5) = 2//3//5//11//7 = 235117 = prime(20845).
a(20) = 7//5//11//2//3 = 751123 = prime(60315).

Cf. A000040, A033548, A134966, A177061.

catL := proc(L) local a,i,dgs ; a := op(1,L) ; for i from 2 to nops(L) do dgs := max(1, 1+ilog10(op(i,L))) ; a := a*10^dgs+op(i,L) ; end do: a ; end proc:
A177275 := proc() local pL,a,c ; pL := [seq(ithprime(c),c=1..5)] ; a := {} ; for c in combinat[permute](pL) do p := catL(c) ; if isprime(p) then a := a union {p} ; end if; end do: print(sort(a)) ; end proc:
A177275() ; # R. J. Mathar, May 09 2010

Added keyword:base,full. Removed the variable p. - R. J. Mathar and Zak Seidov, May 09 2010

A090433 Primes p(k) having a smaller sum of digits than k.

Original entry on oeis.org

11, 13, 23, 61, 101, 103, 107, 109, 151, 163, 211, 223, 227, 241, 251, 271, 311, 313, 317, 331, 337, 347, 401, 421, 431, 433, 443, 461, 503, 509, 521, 523, 701, 911, 1009, 1013, 1021, 1031, 1033, 1051, 1061, 1063, 1103, 1109, 1117, 1123, 1129, 1151

Offset: 1

Reinhard Zumkeller, Dec 01 2003

A090431(a(n)) > 0.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A033548, A090432, A007953, A007605, A090457.

Select[Prime[Range[200]],Total[IntegerDigits[#]]Harvey P. Dale, Mar 05 2017 *)

cp's OEIS Frontend

A259067 Sum of digits of Honaker primes (A033548).

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A151993 Number of Honaker primes (A033548) less than 10^n.

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A161118 Honaker emirps: terms in A033548 that are emirps.

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A161197 Smallest Honaker prime A033548 with digit sum prime(n), or 0 if no such prime exists.

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A033549 Numbers k such that sum of digits of k-th prime equals sum of digits of k.

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A072439 Primes prime(k) such that the number of binary 1's in prime(k) equals the number of binary 1's in k.

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

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A176111 Honaker primes of the form p = 2*k-1 with sum-of-digits(p) = sum-of-digits(k).

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