A218448 First of a run of 5 consecutive numbers with same prime signature.

204323, 3252571, 5205074, 7201674, 20182921, 28387953, 36193650, 43216722, 51049537, 56155074, 57070850, 61961315, 62167075, 65425473, 76647074, 82507473, 92658049, 95943321, 100498849, 107236449, 109751473, 110899321, 112198075, 112477849, 116736323

Offset: 1

Author

M. F. Hasler, Oct 28 2012

Keywords

• nonn

Comments

A number n is in this sequence iff n and n+1 is in A175590; also: iff n and n+2 are in A052214 (in which case n+1 is in A052214, too); and also: iff {n,n+1,n+2,n+3} are in A052213.

A034173(6) = A218448(62) = A218448(63)-1 is the least term n such that n+1 is also in the sequence.

Links

• M. F. Hasler and Donovan Johnson, Table of n, a(n) for n = 1..1000 (first 140 terms from _M. F. Hasler_)

Crossrefs

Cf. A034173, A034174, A006558, A083790, A052213, A052214, A175590.

Programs

PARI

is_A218448(n)={my(f);!for(i=0,4,f!=(f=vecsort(factor(n+i)[,2])) & i & return)}

PARI

f(k)=vecsort(factor(k)[,2]~,,4)
t=f(n=2);while(n<1e8, for(i=n+1, n+4, tt=f(i); if(tt!=t, n=i; t=tt; next(2))); print1(n", "); n++) \\ Charles R Greathouse IV, Oct 28 2012

Extensions

a(6)-a(8) from Charles R Greathouse IV, Oct 28 2012

a(9)-a(25) from Donovan Johnson, Oct 28 2012

Values up to a(140) computed using b175590.txt from Charles R Greathouse IV - M. F. Hasler, Oct 28 2012