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 1-3 of 3 results.

A289867 Primes obtained from other primes by prefixing a 6.

Original entry on oeis.org

67, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 683, 6101, 6113, 6131, 6151, 6163, 6173, 6197, 6199, 6211, 6229, 6257, 6263, 6269, 6271, 6277, 6311, 6317, 6337, 6353, 6359, 6367, 6373, 6379, 6389, 6397, 6421, 6449, 6491, 6521, 6547, 6563
Offset: 1

Views

Author

Vincenzo Librandi, Jul 15 2017

Keywords

Examples

			613 is a term because it is a prime obtained by prefixing a 6 to the prime 13.
6101 is a term because it is a prime obtained by prefixing a 6 to the prime 101.

Links

Crossrefs

Cf. similar sequences listed in A289866.

Programs

  • Magma
    [k: p in PrimesUpTo(800) | IsPrime(k) where k is Seqint(Intseq(p) cat [6])];
  • Maple
    p:= 0: A:= NULL:
while p < 1000 do
  p:= nextprime(p);
  q:= 10^(ilog10(p)+1)*6+p;
  if isprime(q) then A:= A, q; fi
od:
A; # Robert Israel, Jul 17 2017
  • Mathematica
    Select[Table[FromDigits[Join[IntegerDigits[6], IntegerDigits[Prime[n]]]], {n, 110}], PrimeQ]
Select[6*10^IntegerLength[#]+#&/@Prime[Range[150]],PrimeQ] (* Harvey P. Dale, Apr 03 2022 *)
  • PARI
    terms(n) = my(i=0); forprime(p=1, , my(s=eval(Str(6, p))); if(ispseudoprime(s), print1(s, ", "); i++); if(i==n, break))
/* Print initial 50 terms as follows */
terms(50) \\ Felix Fröhlich, Jul 15 2017

A039790 Prime numbers prefixed with a '1'.

Original entry on oeis.org

12, 13, 15, 17, 111, 113, 117, 119, 123, 129, 131, 137, 141, 143, 147, 153, 159, 161, 167, 171, 173, 179, 183, 189, 197, 1101, 1103, 1107, 1109, 1113, 1127, 1131, 1137, 1139, 1149, 1151, 1157, 1163, 1167, 1173, 1179, 1181, 1191, 1193, 1197, 1199, 1211
Offset: 1

Views

Author

Kevin N. Stone (kevin.stone(AT)brainbashers.com)

Keywords

Comments

Replace every prime by the concatenation of its divisors. [Lekraj Beedassy, May 29 2009]

Links

Crossrefs

Cf. A000040, A037278, A289866 (terms which are prime).

Programs

  • Mathematica
    Array[10^Floor[1 + Log10[#]] + # &@ Prime[#] &, 47] (* Michael De Vlieger, Apr 05 2021 *)
  • PARI
    a(n) = eval(concat(Str(1), Str(prime(n)))) \\ Felix Fröhlich, Apr 05 2021

Formula

a(n) = A037278(A000040(n)). [Lekraj Beedassy, May 29 2009]

A290407 Primes obtained from other primes by prefixing an 8.

Original entry on oeis.org

83, 811, 823, 829, 853, 859, 883, 8101, 8167, 8179, 8191, 8233, 8263, 8269, 8293, 8311, 8317, 8353, 8389, 8419, 8431, 8443, 8461, 8467, 8521, 8563, 8599, 8641, 8647, 8677, 8719, 8761, 8821, 8839, 8863, 8887, 8929, 8941, 8971, 81013, 81019, 81031, 81049, 81097
Offset: 1

Views

Author

K. D. Bajpai, Jul 30 2017

Keywords

Comments

Except a(1), all the terms in this sequence are congruent to 1 mod 3.

Examples

			823 is in the sequence because it is a prime obtained by prefixing an 8 to the prime 23.
8317 is in the sequence because it is a prime obtained by prefixing an 8 to the prime 317.

Links

Crossrefs

Subsequence of A045714.
Cf. A165555, A167187, A289866, A289867.

Programs

  • Magma
    [k : p in PrimesUpTo (5000) | IsPrime (k) where k is Seqint (Intseq (p) cat Intseq (8))];
  • Maple
    A290407:= n-> (parse(cat(8, ithprime(n)))): select(isprime, [seq((A290407 (n), n=1..1000))]);
  • Mathematica
    Select[k = 8; Table[FromDigits[Join[IntegerDigits[k], IntegerDigits[Prime[n]]]], {n, 500}], PrimeQ]
  • PARI
    forprime(p = 2,5000, k=eval(concat(8,Str(p))); if(isprime(k), print1(k,", ")));
Showing 1-3 of 3 results.

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

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