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 1-7 of 7 results.

A280993 Primes such that the absolute value of the difference between the largest digit and the sum of all the other digits is a cube.

Original entry on oeis.org

11, 19, 23, 43, 67, 89, 101, 109, 113, 131, 157, 167, 179, 197, 199, 211, 223, 241, 257, 263, 269, 311, 313, 331, 337, 347, 353, 359, 373, 379, 397, 421, 431, 449, 461, 463, 523, 541, 571, 593, 607, 617, 641, 643, 661, 683, 719, 733, 739, 743
Offset: 1

Views

Author

Osama Abuajamieh, Jan 14 2017

Keywords

Comments

If the largest digit L (say) is repeated, the criterion is that |L - (sum of all digits except for one copy of L)| is a cube.

Examples

			The prime 2731 is a term, because 7-2-3-1 = 1 is a cube.
The prime 13 is not in the sequence, as 3-1 = 2, and 2 is not a cube.
The prime 313 is a term because |3 - (1+3)| = 1 is a cube.

Links

Crossrefs

A156753 and A156979 are subsequences.

Programs

  • Mathematica
    Select[Prime[Range[150]],IntegerQ[Surd[Abs[Max[IntegerDigits[#]]-Total[ Most[ Sort[IntegerDigits[#]]]]],3]]&] (* Harvey P. Dale, Dec 31 2021 *)
  • PARI
    listA280993(k, {k0=5})={my(H=List(), y); forprime(z=prime(k0), prime(k), y=digits(z); if(ispower(abs(vecsum(y)-2*vecmax(y)),3), listput(H, z))); return(vector(#H, i, H[i]))} \\ Looks for those belonging terms between prime(k0) and prime(k). - R. J. Cano, Feb 06 2017

A158281 Prime numbers p such that prime = abs(smallest digit of p - sum of all the other digits of p).

Original entry on oeis.org

2, 3, 5, 7, 13, 29, 31, 41, 47, 53, 61, 79, 83, 97, 101, 113, 131, 139, 151, 157, 193, 199, 211, 223, 227, 241, 263, 269, 311, 313, 331, 337, 353, 359, 373, 379, 397, 401, 409, 421, 443, 463, 487, 557, 571, 593, 599, 601, 607, 643, 661, 683, 733, 739, 751, 773
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Mar 15 2009, May 25 2009

Keywords

Examples

			13(2=abs(1-3)), 29(7=abs(2-9)), 31(2=3-1)

Links

Crossrefs

Cf. A000040, A156979.

Programs

  • Mathematica
    sdsodQ[n_]:=Module[{sidn=Sort[IntegerDigits[n]]},PrimeQ[Abs[sidn[[1]]-Total[Rest[sidn]]]]]; Select[Prime[Range[150]],sdsodQ] (* Harvey P. Dale, Feb 01 2015 *)

Extensions

Single-digit primes added, duplicates of 421 and 443 removed - R. J. Mathar, May 19 2010

A158283 Prime numbers p such that 1 = abs(final digit of p - sum of all the other digits of p).

Original entry on oeis.org

23, 43, 67, 89, 113, 157, 179, 199, 223, 269, 313, 337, 359, 379, 449, 607, 719, 739, 809, 829, 919, 1013, 1033, 1103, 1123, 1213, 1237, 1259, 1279, 1303, 1327, 1439, 1459, 1549, 1619, 1709, 2003, 2069, 2089, 2113, 2137, 2179, 2203, 2269, 2339, 2539
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Mar 15 2009

Keywords

Examples

			23(1=3-2), 43(1=abs(3-4)), 67(1=abs(7-6)), 89(1=abs(9-8)), 113(1=3-(1+1)).

Links

Crossrefs

Cf. A000040, A156979.
Cf. also A062339, A062341, A062337, A062343, A107579.

Programs

  • Mathematica
    ps1[n_]:=Module[{idn=IntegerDigits[n]},Abs[Last[idn]-Total[Most[idn]]] == 1]; Select[Prime[Range[400]],ps1] (* Harvey P. Dale, Jul 31 2012 *)

Extensions

Entries checked by R. J. Mathar, May 19 2010

A156980 Primes p such that 2 = abs(largest digit of p - sum of all the other digits of p).

Original entry on oeis.org

2, 13, 31, 53, 79, 97, 103, 163, 233, 251, 277, 349, 367, 383, 389, 433, 439, 457, 479, 503, 521, 547, 563, 569, 613, 619, 631, 653, 659, 673, 691, 709, 727, 839, 907, 929, 947, 983, 1063, 1069, 1151, 1223, 1249, 1283, 1289, 1423, 1429, 1447, 1481, 1511
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Feb 20 2009

Keywords

Crossrefs

Cf. A000040, A156979.

Extensions

Removed 1033. Inserted 1069. R. J. Mathar, Feb 22 2009

A157009 Primes p such that 3 = abs(largest digit of p - sum of all the other digits of p).

Original entry on oeis.org

3, 41, 47, 137, 151, 173, 227, 283, 317, 401, 443, 467, 487, 557, 647, 773, 823, 883, 1051, 1217, 1277, 1307, 1367, 1381, 1433, 1453, 1543, 1637, 1721, 1783, 1831, 1873, 2027, 2083, 2207, 2221, 2243, 2267, 2281, 2287, 2357, 2423, 2441, 2447, 2551, 2683
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Feb 21 2009

Keywords

Comments

Since zero digits are allowed, sequence is almost certainly infinite. - Zak Seidov, Feb 22 2009

Examples

			a(1)=3 because 3=abs(3-0). a(4)=137 because 1<3<7 and 3=abs(7-(1+3)).

Crossrefs

Cf. A000040, A156979.

Programs

  • Mathematica
    moQ[n_]:=Module[{idn=IntegerDigits[n]},Abs[2Max[idn]-Total[idn]] ==3]; Select[Prime[Range[500]],moQ] (* Harvey P. Dale, May 12 2011 *)

Extensions

Removed 1481. R. J. Mathar, Feb 21 2009

A158282 Composite numbers k such that prime = abs(smallest digit of k - sum of all the other digits of k).

Original entry on oeis.org

14, 16, 18, 20, 24, 25, 27, 30, 35, 36, 38, 42, 46, 49, 50, 52, 57, 58, 63, 64, 68, 69, 70, 72, 74, 75, 81, 85, 86, 92, 94, 96, 102, 104, 106, 110, 112, 115, 117, 120, 121, 122, 124, 126, 133, 135, 140, 142, 144, 148, 153, 159, 160, 162, 166, 168, 171, 175, 177, 184
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Mar 15 2009, May 25 2009

Keywords

Examples

			14(3=abs(1-4)), 16(5=abs(1-6)), 18(7=abs(1-8)), 20(2=2-0)

Crossrefs

Cf. A000040, A002808, A156979.

Programs

  • Mathematica
    sdkQ[n_]:=Module[{id=IntegerDigits[n],mid},mid=Min[id];PrimeQ[Abs[mid-Total[DeleteCases[ id,mid,1,1]]]]]; cnkQ[n_]:=CompositeQ[n]&&sdkQ[n]; Select[Range[200],cnkQ] (* Harvey P. Dale, Aug 23 2024 *)

Extensions

Entries checked by R. J. Mathar, May 19 2010

A281170 Primes p whose decimal representation satisfy: abs(digsum(p)-2*L(p)) = 8, being L(p) the largest decimal digit in p.

Original entry on oeis.org

19, 109, 1009, 1777, 1889, 1979, 1997, 2677, 2699, 2767, 2789, 2879, 2897, 2969, 3779, 3797, 4567, 4657, 4679, 4967, 5399, 5557, 5647, 5669, 5737, 5849, 5939, 6277, 6299, 6367, 6389, 6547, 6563, 6569, 6637, 6653, 6659, 6673, 6763, 6947, 6983, 7177
Offset: 1

Views

Author

Osama Abuajamieh, Jan 16 2017

Keywords

Examples

			a(4) = 1777, since abs(digsum(1777)-2*L(1777)) = abs(A007953(1777)-2*A054055(1777)) is 8 and among the primes 1777 is the 4th element satisfying such condition.

Crossrefs

Subsequence of A280993.
Cf. A007953, A054055, A156753, A156979.

Programs

  • Mathematica
    Select[Prime@ Range[10^3], Abs[Max@ # - Total@ Rest@ #] == 8 &@ Reverse@ Sort@ IntegerDigits@ # &] (* Michael De Vlieger, Feb 02 2017 *)
  • PARI
    listA281170(k,{k0=8})={my(H=List(),y);forprime(z=prime(k0),prime(k),y=digits(z);if(abs(vecsum(y)-2*vecmax(y))==8,listput(H,z)));return(vector(#H,i,H[i]))} \\ Looks for those belonging terms between prime(k0) and prime(k). - R. J. Cano, Feb 06 2017
Showing 1-7 of 7 results.

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