A340112 Prime-acronym numbers: sums of primes which also equal the concatenation of the initial digits of these primes.

2, 3, 5, 7, 21, 32, 117, 119, 127, 131, 132, 133, 135, 137, 139, 149, 151, 157, 169, 171, 172, 173, 175, 177, 179, 187, 211, 212, 213, 215, 217, 218, 221, 231, 232, 233, 235, 237, 251, 253, 271, 272, 273, 275, 277, 281, 311, 319, 321, 322, 323, 325, 327, 329, 331

Offset

1,1

Links

Table of n, a(n) for n=1..55.

Eric Angelini, Sum of peculiar primes, math-fun mailing list, Dec 24, 2020.

Example

Single-digit primes trivially satisfy the constraint.
21 is the sum and also concatenation of the initial digits of the primes 2 and 19.
32 is the sum and also concatenation of the initial digits of the primes 3 and 29.
117 is the sum and also concatenation of the initial digits of the primes 19, 19 and 79.

Prog

(PARI) is_A340112(n, d=digits(n), nd=if(vecmin(d), #d))={ /* Check whether n is the sum of primes starting with the digits d[1..nd], respectively. If there's a zero digit, return 0. If there's a single digit left, n must be a prime starting with d[1] */ nd<2 && return(isprime(n) && nd && d[1]==digits(n)[1]); /* else subtract from n a prime p starting with digit d[nd]; check n-p with digits d[1 .. nd-1] */ for( e= !isprime(d[nd]), logint(n, 10), forprime( p=d[nd]*10^e, min(n-vecsum(d[^-1]), (d[nd]+1)*10^e-1), self()(n-p, d[^-1], nd-1) && return(1)))}

Crossrefs

Cf. A340113 for the subset of primes in this sequence.

Sequence in context: A162948 A024768 A024769 * A376776 A085557 A125665

Adjacent sequences: A340109 A340110 A340111 * A340113 A340114 A340115

Keyword

nonn,base

Author

Eric Angelini and M. F. Hasler, Dec 28 2020

Status

approved