A330536 The partial sum a(1)+...+a(n) is prime, and so is the sum of the digits used by those n terms.

2, 1, 4, 6, 24, 22, 8, 42, 28, 60, 26, 46, 44, 40, 68, 66, 112, 158, 64, 86, 84, 118, 62, 88, 20, 48, 156, 114, 136, 138, 132, 150, 116, 82, 192, 176, 190, 392, 198, 172, 152, 178, 240, 206, 174, 282, 244, 80, 154, 242, 204, 202, 228, 170, 246, 130, 648, 110, 756, 196, 194, 222, 208, 266, 286, 284, 280, 200

Offset: 1

Author

Eric Angelini and Carole Dubois, Dec 17 2019

Keywords

• base
• nonn

Comments

This is the lexicographically earliest sequence of distinct numbers > 0 with this property.

Examples

			The successive partial sums of terms are prime:
(2), (2 + 1) = 3, (2 + 1 + 4) = 7; (2 + 1 + 4 + 6) = 13; (2 + 1 + 4 + 6 + 24) = 37; etc.
The successive partial sums of their digits are also prime:
(2), (2 + 1) = 3, (2 + 1 + 4) = 7; (2 + 1 + 4 + 6) = 13; (2 + 1 + 4 + 6 + 2 + 4) = 19; etc.
		

Links

• Carole Dubois, Table of n, a(n) for n = 1..5000
• Carole Dubois, Graph and trend curves for terms, digits sums, terms sums
• Rémy Sigrist, C++ program for A330536

Crossrefs

Cf. A054408 (smallest positive integer not already in sequence such that the partial sum a(1)+...+a(n) is prime).

Programs

Mathematica

Nest[Append[#, Block[{k = 1}, While[Nand[FreeQ[#, k], PrimeQ[Total@ # + k], PrimeQ@ Total@ Flatten@ IntegerDigits[Append[#, k]]], k++]; k]] &, {}, 68] (* Michael De Vlieger, Dec 17 2019 *)