A360929 - OEIS

A360929

Odd numbers which cannot be expressed as p + q*(q+1) where p and q are primes.

1, 3, 5, 7, 21, 27, 39, 45, 51, 57, 81, 105, 111, 141, 147, 171, 177, 231, 273, 303, 315, 351, 357, 471, 501, 525, 567, 585, 735, 741, 761, 771, 831, 849, 861, 897, 945, 1017, 1083, 1161, 1197, 1281, 1343, 1407, 1475, 1521, 1525, 1575, 1695, 1767, 1997, 2151

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OFFSET

1,2

COMMENTS

It is conjectured that 1446377 is the largest term.

q*(q+1) is even which implies that p must be an odd prime.

The expression p + q*(q+1) resembles the expression p + 2*q used in Lemoine's conjecture.

LINKS

Marc Ridders, Table of n, a(n) for n = 1..167

MATHEMATICA

a[1]=1; a[n_]:=a[n]=(k=a[n-1]; c=True; While[c, k=k+2; c=False; q=2; While[!c&&q*(q+1)<k, p=k-(q*(q+1)); c=PrimeQ[p]; q=NextPrime[q]]]; k); Table[a[n], {n, 1, 167}]

CROSSREFS

Cf. A360930, A046927.

Sequence in context: A352710 A163637 A336985 * A228068 A182233 A370204

Adjacent sequences: A360926 A360927 A360928 * A360930 A360931 A360932

KEYWORD

easy,nonn

AUTHOR

Marc Ridders, Feb 25 2023

STATUS

approved