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.

A106754 Primes p with digital sum equal to 11.

Original entry on oeis.org

29, 47, 83, 137, 173, 191, 227, 263, 281, 317, 353, 443, 461, 641, 821, 911, 1019, 1091, 1109, 1163, 1181, 1217, 1307, 1361, 1433, 1451, 1523, 1613, 1721, 1811, 1901, 2027, 2063, 2081, 2153, 2207, 2243, 2333, 2351, 2423, 2441, 2531, 2621, 2711, 2801, 3251
Offset: 1

Views

Author

Zak Seidov, May 16 2005

Keywords

Links

Crossrefs

Cf. A000040 (primes), A007953 (sum of digits), A166311 (digit sum = 11).
Cf. A062339 (same for digit sum s = 4), ..., A107579 (s = 10), A106755 (s = 13), and others listed in A244918 (s = 68).
Subsequence of A119891 (prime trios: chain of prime sums of digits; also has as subsequence A106762 (s = 23), A106774 (s = 41), etc).

Programs

  • Magma
    [p: p in PrimesUpTo(10000) | &+Intseq(p) eq 11]; // Vincenzo Librandi, Jul 08 2014
  • Mathematica
    Select[Prime[Range[100000]], Total[IntegerDigits[#]]==11 &] (* Vincenzo Librandi, Jul 08 2014 *)
  • PARI
    select( {is_A106754(n)=sumdigits(n)==11&&isprime(n)}, primes([1, 3333])) \\ M. F. Hasler, Mar 09 2022

Formula

Intersection of A000040 (primes) and A166311 (digit sum = 11), also equals { p in A000040 | A007953(p) = 11 }. - M. F. Hasler, Mar 09 2022

A119892 Prime quartet leaders: largest number of a prime quartet.

Original entry on oeis.org

2999, 3989, 4799, 4889, 5879, 5897, 5987, 6599, 6689, 6779, 6869, 6959, 6977, 7499, 7589, 7877, 7949, 8597, 8669, 8849, 8867, 9479, 9497, 9587, 9677, 9749, 9767, 9839, 9857, 9929, 12899, 13799, 13997, 14699, 14879, 14897, 14969, 15797, 15887, 15959
Offset: 1

Views

Author

Luc Stevens (lms022(AT)yahoo.com), May 27 2006

Keywords

Comments

A prime quartet is a set of four different prime numbers such that the fourth number is a 1-digit number which is the sum of the digits of the third number, the third number is the sum of the digits of the second number and the second number is the sum of the digits of the first number.
Different from A106766.
Comment from Joshua Zucker, Apr 24 2007, on the difference between this sequence and A106766: The digit sum must be the largest member of a prime trio, so the first number where the sequences differ must be with digit sum 47 and thus have at least 6 digits - so until then you get all the primes with 4 or 5 digits that have digit sum 29.
a(2322)=389999 is the first value different from A106766, where A106766(2322)=390359. See also A106778 = primes with digit sum = 47: A106778(1)=389999. - Martin Fuller and Ray Chandler, Apr 24 2007
The sequence of prime quintet leaders is probably too large for the OEIS; its first term is the 334-digit prime 5*10^333-10^330-10^328-1 with sum of digits a(1) = 2999. - Charles R Greathouse IV, Mar 11 2022

Examples

			2999 is in the sequence because it is the largest number of the prime quartet (2999,29,11,2).

Links

Crossrefs

Cf. A119889, A119890, A119891.

Programs

  • Mathematica
    pqQ[n_]:=Module[{p1=NestList[Total[IntegerDigits[#]]&,n,3]},AllTrue[ Take[ p1,3],#>9&]&&AllTrue[p1,PrimeQ]]; Select[Range[16000],pqQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 02 2020 *)
  • PARI
    DigitSum(n,b=10)=local(x);x=0;while(n,x+=n%b;n\=b);x
PrimeEnsemble(n,b=10)=local(x);x=1;while(ispseudoprime(n),if(n=4, print1(p", "))); \\ Martin Fuller

A119889 Prime soloist : prime number which is no member of any prime ensemble.

Original entry on oeis.org

3, 13, 17, 19, 31, 37, 53, 59, 67, 71, 73, 79, 89, 97, 103, 107, 109, 127, 139, 149, 157, 163, 167, 179, 181, 193, 197, 199, 211, 229, 233, 239, 251, 257, 269, 271, 277, 283, 293, 307, 337, 347, 349, 359, 367, 373, 379, 383, 389, 397, 409, 419, 431, 433, 439
Offset: 1

Views

Author

Luc Stevens (lms022(AT)yahoo.com), May 27 2006

Keywords

Examples

			17 is in the sequence because the sum of the digits (8) is a composite number. 449 is in the sequence because the sum of the digits (17) is another prime soloist.

Links

Crossrefs

Cf. A119890, A119891, A119892.

Extensions

Corrected by T. D. Noe, Oct 25 2006

A119890 Prime duet leaders: largest number of a prime duet.

Original entry on oeis.org

11, 23, 41, 43, 61, 101, 113, 131, 151, 223, 241, 311, 313, 331, 401, 421, 601, 1013, 1031, 1033, 1051, 1103, 1123, 1213, 1231, 1301, 1303, 1321, 2003, 2111, 2113, 2131, 2203, 2221, 2311, 3011, 3121, 3301, 4001, 4003, 4021, 4111, 4201, 5011, 5101, 10103
Offset: 1

Views

Author

Luc Stevens (lms022(AT)yahoo.com), May 27 2006

Keywords

Comments

A prime duet is a pair of two different prime numbers such that the second number is a 1-digit number which is the sum of the digits of the first number.
The terms of the sequence must be at least 2 digits in length, so {5,5} is not a prime duet. - Harvey P. Dale, May 07 2021

Examples

			113 is in the sequence because it is the largest number of the prime duet (113,5)

Links

Crossrefs

Cf. A119889, A119891, A119892.

Programs

  • Mathematica
    Select[Prime[Range[5,1300]],IntegerLength[Total[IntegerDigits[#]]]==1&&PrimeQ[Total[IntegerDigits[#]]]&] (* Harvey P. Dale, May 07 2021 *)
  • PARI
    \\ See PARI link. David A. Corneth, May 07 2021

Extensions

Corrected by Harvey P. Dale, May 07 2021
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.