A062241 Smallest integer >= 2 that is not the sum of 2 positive integers whose prime factors are all <= prime(n), the n-th prime.

3, 7, 23, 71, 311, 479, 1559, 5711, 10559, 18191, 31391, 118271, 366791, 366791, 2155919, 2155919, 2155919, 6077111, 6077111, 98538359, 120293879, 131486759, 131486759, 508095719, 2570169839, 2570169839, 2570169839, 2570169839, 2570169839, 2570169839

Offset

0,1

Comments

Here we are taking 1 to be the zeroth prime.

Computed by David W. Wilson, Jun 29 2001

a(30) > 2570169839. - Donovan Johnson, Aug 31 2010

Links

Table of n, a(n) for n=0..29.

Thomas F. Bloom, Erdős Problem #334

Touch Sungkawichai, Proof that bounded A045535

Formula

a(n) <= A045535(n-1). - Touch Sungkawichai, Mar 05 2026

Example

a(1): 2=1+1, 3=1+2, 4=2+2, 5=1+4, 6=2+4, but 7 cannot be written as the sum of two positive integers whose prime factors are all <= 2, so a(1) = 7.
a(2): 7=3+4, 8=4+4, 9=1+8, ..., 22=4+18, but 23 cannot be so written, so a(2) = 23.

Crossrefs

So far it agrees with A045535. Is this a coincidence or a theorem?

Sequence in context: A140456 A066768 A225914 * A000229 A133435 A079061

Adjacent sequences: A062238 A062239 A062240 * A062242 A062243 A062244

Keyword

nonn,nice

Author

Richard C. Schroeppel, Jun 27 2001

Extensions

More terms from Jud McCranie, Nov 01 2001

a(23)-a(29) from Donovan Johnson, Aug 31 2010

Status

approved