A002200 Primes of the form 2^q*3^r*5^s + 1. (Formerly M0654 N0242)

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

1,1

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)

Mathematica

up=10^6; a=1; Sort[Reap[While[ a<up, b=a; While[ b<up, c=b; While[ c<up, If[ PrimeQ[ c+1], Sow[ c+1]]; c *= 5]; b *= 3]; a *= 2]][[2, 1]]] (* Giovanni Resta, Jul 18 2017 *)

Prog

(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(c<n, i++; if(isprime(v[i]+1), c++; print(c" "v[i]+1))); } \\ Jean-Marie Madiot, Jul 17 2017
(Magma) [p: p in PrimesUpTo(5000) | forall{d: d in PrimeDivisors(p-1) | d le 5}]; // Bruno Berselli, Sep 24 2012
(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

Crossrefs

Cf. A174144, A005109, A077497.

Sequence in context: A293667 A068192 A225083 * A181561 A216496 A069709

Adjacent sequences: A002197 A002198 A002199 * A002201 A002202 A002203

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved