A287662 a(n) is the smallest positive integer not already in sequence such that a(1) + ... + a(n) is a prime power, with a(1) = 1.

1, 2, 4, 6, 3, 7, 8, 10, 12, 11, 9, 16, 14, 18, 28, 20, 22, 32, 33, 13, 24, 38, 30, 36, 34, 26, 42, 48, 40, 44, 46, 50, 60, 52, 68, 54, 58, 5, 15, 64, 78, 56, 66, 70, 74, 76, 84, 62, 72, 82, 90, 80, 55, 21, 92, 106, 104, 88, 98, 100, 96, 108, 102, 86, 114, 94, 116, 118, 122, 120, 130, 126, 107, 31, 132, 138

Offset: 1

Author

Ilya Gutkovskiy, May 29 2017

Keywords

• nonn

Comments

It appears that the sequence contains all even numbers.

Examples

			a(8) = 10 because 1, 2, 3, 4, 6, 7 and 8 have already been used in the sequence, 1 + 2 + 4 + 6 + 3 + 7 + 8 + 5 = 36 is not prime power, 1 + 2 + 4 + 6 + 3 + 7 + 8 + 9 = 40 is not prime power while 1 + 2 + 4 + 6 + 3 + 7 + 8 + 10 = 41 is a prime power.
		

Crossrefs

Cf. A000961, A054408, A073659, A073879, A075562, A084693, A284049.

Programs

Mathematica

t = {1}; Do[i = 1; While[! PrimePowerQ[Total[t] + i] || MemberQ[t, i], i++]; AppendTo[t, i], {75}]; t