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 1-4 of 4 results.

A082283 Duplicate of A065867.

Original entry on oeis.org

5, 23, 31, 41, 53, 59, 67, 71, 83, 97, 101, 109, 131, 139, 173, 181, 197, 199, 211, 223, 233, 251, 263, 269, 271, 281, 311, 331, 349, 353, 373, 401, 421, 431, 439, 443, 449, 457, 463, 487, 491, 499, 503, 523, 563, 587, 593, 607, 617, 631, 647, 659, 661, 677
Offset: 1

Views

Author

Cino Hilliard, May 09 2003

Keywords

A158754 Courteous prime numbers.

Original entry on oeis.org

31, 41, 101, 109, 137, 191, 193, 239, 283, 311, 313, 569, 641, 659, 661, 821, 1091, 1153, 1289, 1291, 1301, 1303, 1319, 1429, 1453, 1619, 1667, 1877, 2027, 2081, 2129, 2239, 2309, 2341, 2381, 2591, 2593, 2711, 2713, 2971, 3001, 3121, 3253, 3299, 3301
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 25 2009

Keywords

Comments

Courteous prime numbers are twin prime numbers and can be written as the sum of two or more consecutive twin prime numbers. 7+11+13=31,11+13+17=41,..

Crossrefs

Cf. A138591, A065867

Programs

  • Mathematica
    lst={};Do[pp=Prime[m];If[PrimeQ[pp-2]||PrimeQ[pp+2],k=1;Do[k++;p=Prime[n];If[PrimeQ[p-2]||PrimeQ[p+2],pp+=p;If[PrimeQ[pp],If[PrimeQ[pp-2]||PrimeQ[pp+2],AppendTo[lst,pp]]]],{n,m+1,4*6!}]],{m,1,4*6!}];lst;(*Courteous Prime Numbers.*)Take[Union[lst],5! ]
upto=3400;With[{tps=Union[Flatten[Select[Partition[Prime[Range[ PrimePi[ upto]]], 2,1], Last[#]-First[#]==2&]]]}, Select[Union[Flatten[Table[ Total/@Partition[tps,n,1],{n,2,40}]]],MemberQ[tps,#]&&#<=upto&]] (* Harvey P. Dale, Sep 25 2011 *)

A066366 Primes which are the sum of a prime number of consecutive primes in a prime number of different ways.

Original entry on oeis.org

83, 199, 223, 251, 857, 863, 883, 941, 983, 991, 1061, 1151, 1187, 1283, 1367, 1381, 1433, 1439, 1523, 1553, 1607, 1753, 1901, 2011, 2179, 2357, 2393, 2647, 2689, 2731, 2777, 2837, 2927, 2963, 3037, 3121, 3181, 3617, 3821, 3853, 3911, 3967, 4217, 4337
Offset: 1

Views

Author

Henry Bottomley, Dec 21 2001

Keywords

Examples

			199 is on the list because it can be written in two (prime) ways as the sum of either three (prime) or five (prime) consecutive primes: 61+67+71 = 31+37+41+43+47.
311 is not on the list because it can be written as the sum of three, five, seven, or eleven consecutive primes: four (not prime) ways. - _Hans Havermann_, Mar 24 2018

Links

Crossrefs

Cf. A065867.

A158758 Politest numbers.

Original entry on oeis.org

4, 8, 9, 11, 13, 14, 15, 16, 18, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 33, 35, 36, 37, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 89, 90
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 25 2009

Keywords

Comments

Politest numbers can be written as the sum of two or more consecutive polite numbers. 1,3,5,6,7,9,10,11,12,13,14,15,17,18,...Polite numbers. 4=1+3, 8=3+5, 9=1+3+5, 11=5+6, 13=6+7, 14=3+5+6, 15=1+3+5+6,...Politest numbers.

Crossrefs

Cf. A138591, A065867, A158754

Programs

  • Mathematica
    lst={};Do[p=m;If[Mod[2^p,p]!=0||p==1,Do[If[Mod[2^n,n]!=0,p+=n;AppendTo[lst,p]],{n,m+1,5!}]],{m,1,5!}];Take[Union[lst],5! ]
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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