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.

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A117745 Prime Fibonacci numbers that are not Chen primes.

Original entry on oeis.org

1597, 28657, 433494437, 2971215073, 99194853094755497, 1066340417491710595814572169, 19134702400093278081449423917
Offset: 0

Views

Author

Jani Melik, Apr 28 2006

Keywords

Crossrefs

Cf. A005478, A109611.

Programs

  • Maple
    ischenprime:=proc(n); if (isprime(n) = 'true') then if (isprime(n+2) = 'true' or numtheory[bigomega](n+2) = 2) then RETURN('true') else RETURN('false') fi fi end: ts_prime_fibonacci_notchen:=proc(n) local i, tren, ans; ans:= [ ]: for i from 0 to n do tren := combinat[fibonacci](i): if (isprime( tren ) = 'true' and ischenprime(tren) = 'false') then ans:=[op(ans), tren]: fi od; return ans end: ts_prime_fibonacci_notchen(300); # Jani Melik, May 05 2006

A118483 Partial sums of primes that are not Chen primes (starting with 1).

Original entry on oeis.org

1, 44, 105, 178, 257, 354, 457, 608, 771, 944, 1137, 1360, 1589, 1830, 2101, 2378, 2661, 2974, 3305, 3654, 4021, 4394, 4777, 5174, 5595, 6028, 6467, 6924, 7387, 7910, 8457, 9050, 9651, 10258, 10871, 11490, 12133, 12794, 13467, 14158, 14867, 15594
Offset: 0

Views

Author

Jani Melik, May 05 2006

Keywords

Crossrefs

Cf. A014284, A102540, A109611.

Programs

  • Maple
    ischenprime:=proc(n); if (isprime(n) = 'true') then if (isprime(n+2) = 'true' or numtheory[bigomega](n+2) = 2) then RETURN('true') else RETURN('false') fi fi end: ts_partsum_notchenprime:=proc(n) local i,ans,tren; ans:=1: tren:=1: for i from 1 to n do if (ischenprime(i)='false') then tren := tren+i: ans:=[op(ans), tren]: fi od; RETURN(ans) end: ts_partsum_notchenprime(1000);
  • Mathematica
    Accumulate[Join[{1},Select[Prime[Range[200]],PrimeOmega[#+2]>2&]]] (* Harvey P. Dale, Dec 14 2012 *)

A118491 Product of first n Chen primes.

Original entry on oeis.org

1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230, 200560490130, 7420738134810, 304250263527210, 14299762385778870, 757887406446280110, 44715356980330526490, 2995928917682145274830
Offset: 0

Views

Author

Jani Melik, May 05 2006

Keywords

Comments

This first differs from primorials A002110 at a(14) = 14299762385778870 = 47*a(13) rather than 43*a(13) because 43 is the smallest prime that is not a Chen prime (A102540). - Jonathan Vos Post, Dec 25 2008

Examples

			a(0) = 1 by definition. a(1) = 2, 2 is first Chen prime, a(2) = 6 since it is the product of the first two Chen primes 2 and 3, ...

Crossrefs

Cf. A002110, A109611.
Cf. A102540. - Jonathan Vos Post, Dec 25 2008

Programs

  • Maple
    ischenprime:=proc(n); if (isprime(n) = 'true') then if (isprime(n+2) = 'true' or numtheory[bigomega](n+2) = 2) then RETURN('true') else RETURN('false') fi fi end: ts_chen_prim_numbers:=proc(n) local i,ans,tren; ans:=[1]: tren:=1: for i from 1 to n do if (ischenprime(i) = 'true') then tren := i*tren: ans:=[op(ans), tren]: fi od; RETURN(ans) end: ts_chen_prim_numbers(140);
  • Mathematica
    FoldList[Times,Join[{1},Select[Prime[Range[50]],PrimeOmega[#+2]<3&]]] (* Harvey P. Dale, Jun 06 2022 *)

A118494 Palindromic primes that are not Chen primes.

Original entry on oeis.org

151, 313, 373, 383, 727, 757, 929, 10501, 11311, 12421, 13831, 14341, 15451, 17971, 18181, 18481, 19391, 19891, 30103, 30203, 30403, 30703, 30803, 31513, 32323, 32423, 33533, 34543, 34843, 35053, 35153, 35353, 36563, 37273, 37573, 38083
Offset: 1

Views

Author

Jani Melik, May 05 2006

Keywords

Crossrefs

Cf. A002385, A109574, A109611.

Programs

  • Maple
    # Check if number is Chen prime ischenprime:=proc(n); if (isprime(n) = 'true') then if (isprime(n+2) = 'true' or numtheory[bigomega](n+2) = 2) then return 'true' else return 'false' fi fi end: # Check if number is palindrome ts_numpal:=proc(n) local ad; ad:=convert(n, base, 10): if (ListTools[Reverse](ad)=ad) then return 'true' else return 'false' fi end: ts_pal_nonchen:=proc(n) local i,ans; ans:=[ ]: for i from 1 to n do if (ischenprime(i) = 'false' and ts_numpal(i) = 'true') then ans:=[op(ans),i]: fi od: return ans end: ts_pal_nonchen(100000);
  • Mathematica
    Select[ Prime[ Range[5000]], PalindromeQ [#]&&!PrimeQ[ # + 2] &&!PrimeOmega[ #+2]==2 &] (* James C. McMahon, Mar 29 2024 *)

A118495 Chen primes written backwards.

Original entry on oeis.org

2, 3, 5, 7, 11, 31, 71, 91, 32, 92, 13, 73, 14, 74, 35, 95, 76, 17, 38, 98, 101, 701, 901, 311, 721, 131, 731, 931, 941, 751, 761, 971, 181, 191, 791, 991, 112, 722, 332, 932, 152, 752, 362, 962, 182, 392, 703, 113, 713, 733, 743, 353, 953, 973, 983, 104, 904
Offset: 1

Views

Author

Jani Melik, May 05 2006

Keywords

Crossrefs

Cf. A004087, A109611.

Programs

  • Maple
    # Check if number is Chen prime ischenprime:=proc(n); if (isprime(n) = 'true') then if (isprime(n+2) = 'true' or numtheory[bigomega](n+2) = 2) then return 'true' else return 'false' fi fi end: #Reverse digits obrni_stev:=proc(n) local i, tren, tren1, st, ans; ans:=[ ]: tren:=n: tren1:=0: for i while (tren>0) do st:=round(10*frac(tren/10)): ans:=[op(ans), st]: tren:=trunc(tren/10): od: for i from 0 to nops(ans)-1 do tren1:= tren1 + op(nops(ans)-i, ans)*10^(i): od: return tren1 end: ts_inv_chen_pra:= proc(n) local i, trens, ans; trens:= [ ]; ans:=[ ]; for i from 1 to n do if (ischenprime( i ) = 'true') then ans:=[op(ans),obrni_stev(i)] fi: od: return ans end: ts_inv_chen_pra(2000);
  • Mathematica
    psp=Take[Union[Join[Union[Times@@@Tuples[Prime[Range[100]],{2}]],Prime[Range[PrimePi[250000]]]]],200];
FromDigits[Reverse[IntegerDigits[#]]]&/@(Select[Prime[Range[PrimePi[1000]]],MemberQ[psp,#+2]&])  (* Harvey P. Dale, Feb 08 2011 *)

A118496 Reverse digits of largest Chen primes, append to sequence if result is larger Chen prime then previous one with reverse digits.

Original entry on oeis.org

2, 3, 5, 7, 11, 31, 71, 101, 701, 941, 971, 991, 9001, 9011, 9221, 9521, 9941, 70001, 76001, 97001, 99401, 99431, 99571, 99989, 940001, 973001, 987101, 993401, 997811, 999431
Offset: 1

Views

Author

Jani Melik, May 05 2006

Keywords

Comments

Although Chen primes are a subset of primes, this sequence is not a subset of A098922. The first number that is not member of the later is 9011.

Crossrefs

Cf. A004087, A098922, A109611.

Programs

  • Maple
    # Check if number is Chen prime ischenprime:=proc(n); if (isprime(n) = 'true') then if (isprime(n+2) = 'true' or numtheory[bigomega](n+2) = 2) then return 'true' else return 'false' fi fi end: #Reverse digits obrni_stev:=proc(n) local i, tren, tren1, st, ans; ans:=[ ]: tren:=n: tren1:=0: for i while (tren>0) do st:=round(10*frac(tren/10)): ans:=[op(ans), st]: tren:=trunc(tren/10): od: for i from 0 to nops(ans)-1 do tren1:= tren1 + op(nops(ans)-i, ans)*10^(i): od: return tren1 end: ts_inv_prav_chen_pra:= proc(n) local i, tren, ans; tren:=0: ans:=[ ]: for i from 1 to n do if (ischenprime(i)='true' and ischenprime(obrni_stev(i))='true' and obrni_stev(i)>tren) then ans:=[op(ans),obrni_stev(i)]: tren:=obrni_stev(i): fi: od: return ans end: ts_inv_prav_chen_pra(200000);

A118497 Primes that are not Chen primes written backwards.

Original entry on oeis.org

34, 16, 37, 97, 79, 301, 151, 361, 371, 391, 322, 922, 142, 172, 772, 382, 313, 133, 943, 763, 373, 383, 793, 124, 334, 934, 754, 364, 325, 745, 395, 106, 706, 316, 916, 346, 166, 376, 196, 907, 727, 337, 937, 757, 377, 328, 358, 958, 388, 709, 929, 769, 799
Offset: 1

Views

Author

Jani Melik, May 05 2006

Keywords

Crossrefs

Cf. A004087, A102540, A109611.

Programs

  • Maple
    # Check if number is Chen prime ischenprime:=proc(n); if (isprime(n) = 'true') then if (isprime(n+2) = 'true' or numtheory[bigomega](n+2) = 2) then return 'true' else return 'false' fi fi end: #Reverse digits obrni_stev:=proc(n) local i, tren, tren1, st, ans; ans:=[ ]: tren:=n: tren1:=0: for i while (tren>0) do st:=round(10*frac(tren/10)): ans:=[op(ans), st]: tren:=trunc(tren/10): od: for i from 0 to nops(ans)-1 do tren1:= tren1 + op(nops(ans)-i, ans)*10^(i): od: return tren1 end: ts_inv_nonchen_pra:= proc(n) local i, trens, ans; trens:= [ ]; ans:=[ ]; for i from 1 to n do if (ischenprime( i ) = 'false') then ans:=[op(ans),obrni_stev(i)] fi: od: return ans end: ts_inv_nonchen_pra(2000);

A118500 A variation on Flavius's sieves (A000960, A099207): Start with the Chen primes; at the k-th sieving step, remove every (k+1)-st term of the sequence remaining after the (k-1)-st sieving step; iterate.

Original entry on oeis.org

2, 5, 17, 41, 83, 137, 233, 317, 467, 617, 761, 941, 1259, 1427, 1913, 2281, 2531, 2957, 3511, 3797, 4447, 5153, 5351, 6481, 6863, 7669, 8581, 9533, 10259, 11497, 12569, 13441, 14081, 15737, 16187, 17657, 19541, 19991, 21587, 23017, 24317
Offset: 0

Views

Author

Jani Melik, May 05 2006

Keywords

Examples

			Start with
2 3 5 7 11 13 17 19 23 29 31 37 41 47 53 59 67 71 83 89 101 107 109 113 127 131 ... and delete every second term, giving
2 5 11 17 23 31 41 53 67 83 101 109 127 ... and delete every 3rd term, giving
2 5 17 23 41 53 83 101 127 ... and delete every 4th term, giving
.... Continue forever and what's left is the sequence.

Links

Crossrefs

Cf. A000960, A099207, A109611.

Programs

  • Maple
    ts_chen:= proc(n) local i, ans; ans:=[ ]: for i from 1 to n do if ( isprime(i) = 'true') then if ( isprime(i+2) = 'true' or numtheory[bigomega](i+2) = 2) then ans:=[ op(ans), i ] fi fi od: return ans end: S[1]:=convert(ts_chen(25000), set): for n from 2 to 2500 do S[n]:=S[n-1] minus {seq(S[n-1][n*i], i=1..nops(S[n-1])/n)} od: convert(S[2100],list);

A118501 A variation on Flavius's sieves (A099204, A099243): Start with the Chen numbers; at the k-th sieving step, remove every p-th term of the sequence remaining after the (k-1)-st sieving step, where p is the k-th prime; iterate.

Original entry on oeis.org

2, 5, 17, 23, 53, 83, 127, 167, 181, 211, 281, 347, 449, 467, 499, 509, 641, 677, 821, 887, 941, 953, 1097, 1193, 1283, 1327, 1399, 1471, 1583, 1721, 1949, 2029, 2111, 2213, 2351, 2381, 2447, 2549, 2609, 2777, 3061, 3137, 3257, 3307, 3511, 3539, 3797
Offset: 1

Views

Author

Jani Melik, May 05 2006

Keywords

Examples

			Start with
2 3 5 7 11 13 17 19 23 29 31 37 41 47 53 59 67 71 83 89 101 107 109 113 127 131 ... and delete every second term, giving
2 5 11 17 23 31 41 53 67 83 101 109 127 ... and delete every 3rd term, giving
2 5 17 23 41 53 83 101 127 ... and delete every 5th term, giving
2 5 17 23 53 83 101 127
.... Continue forever and what's left is the sequence.

Links

Crossrefs

Cf. A099204, A099243, A109611.

Programs

A118722 Chen primes for which the product of the digits is also a Chen prime.

Original entry on oeis.org

2, 3, 5, 7, 13, 17, 31, 71, 113, 131, 211, 311, 1117, 1151, 1511, 2111, 11117, 11171, 131111, 311111, 511111, 1111151, 1111211, 1111711, 1117111, 11111117, 11111171, 71111111
Offset: 1

Views

Author

Luc Stevens (lms022(AT)yahoo.com), May 21 2006

Keywords

Examples

			31 is in the sequence because (1) it is a Chen prime and (2) the product of its digits 3*1=3 is also a Chen prime.

Crossrefs

Cf. A109611.

Programs

  • Mathematica
    chenQ[n_]:=Module[{pidn=Times@@IntegerDigits[n]},PrimeQ[pidn]&&PrimeOmega[ pidn+2]<3]; With[{chen=Select[Prime[Range[4200000]],PrimeOmega[#+2]<3&]},Select[chen,chenQ]] (* Harvey P. Dale, Apr 22 2012 *)
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