A002200 Primes of the form 2^q*3^r*5^s + 1.

2, 3, 5, 7, 11, 13, 17, 19, 31, 37, 41, 61, 73, 97, 101, 109, 151, 163, 181, 193, 241, 251, 257, 271, 401, 433, 487, 541, 577, 601, 641, 751, 769, 811, 1153, 1201, 1297, 1459, 1601, 1621, 1801, 2161, 2251, 2593, 2917, 3001, 3457, 3889, 4001, 4051, 4801, 4861

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 1, p. 53.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 200 terms from Harry J. Smith)

Crossrefs

Cf. A174144, A005109, A077497.

Programs

GAP

K:=10^7;; # to get all terms <= K.
A:=Filtered([1..K],IsPrime);;
B:=List(A,i->Factors(i-1));;
C:=[];;  for i in B do if Elements(i)=[2] or Elements(i)=[2,3]  or Elements(i)=[2,5] or Elements(i)=[2,3,5]  then Add(C,Position(B,i)); fi; od;
A002200:=Concatenation([2],List(C,i->A[i])); # Muniru A Asiru, Sep 10 2017

Magma

[p: p in PrimesUpTo(5000) | forall{d: d in PrimeDivisors(p-1) | d le 5}]; // Bruno Berselli, Sep 24 2012

Mathematica

up=10^6; a=1; Sort[Reap[While[ aGiovanni Resta, Jul 18 2017 *)

PARI

{ default(primelimit, 16600000); n=0; forprime (p=2, 16600000, m=p-1; p2=p3=p5=0; s=m; r=0; while(r==0, q=s\2; r=s-2*q; s=q; if(r==0, p2++)); s=m; r=0; while(r==0, q=s\3; r=s-3*q; s=q; if(r==0, p3++)); s=m; r=0; while(r==0, q=s\5; r=s-5*q; s=q; if(r==0, p5++)); if (m == 2^p2*3^p3*5^p5, n++; write("b002200.txt", n, " ", p)); if (n >= 200, break); ); } \\ Harry J. Smith, May 25 2009

PARI

{ n=5000; cache=10^5; v=vector(cache); x2=2; x3=3; x5=5; i=j=k=1; v[1]=1; for(m=2,cache,v[m]=t=min(x2,min(x3,x5)); if(x2==t,x2=2*v[i++]); if(x3==t,x3=3*v[j++]); if(x5==t,x5=5*v[k++]);); i=0; c=0; while(cJean-Marie Madiot, Jul 17 2017

Extensions

Better description and more terms from Vladeta Jovovic, May 08 2003